Solved Math Problems Library
Step-by-step solutions for 65+ textbook calculus, derivative, integral, and quadratic problems.
Derivatives with Steps (d/dx)
Power rule, product rule, quotient rule, chain rule, and trig derivatives.
Derivative of x²
Power Rule for Differentiation
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Derivative of x³
Power Rule
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Derivative of sin(x)
Trigonometric Derivative of Sine
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Derivative of cos(x)
Trigonometric Derivative of Cosine
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Derivative of tan(x)
Quotient Rule & Tangent Derivative
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Derivative of eˣ
Exponential Derivative Rule
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Derivative of ln(x)
Natural Logarithm Derivative
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Derivative of √x
Fractional Power Rule
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Derivative of 1/x
Negative Power Rule
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Derivative of 3x² + 5x - 4
Sum & Constant Multiple Rule
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Derivative of x · sin(x)
Product Rule for Differentiation
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Derivative of e^(2x)
Chain Rule for Exponentials
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Derivative of (2x + 1)³
General Power Rule (Chain Rule)
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Derivative of cos(2x)
Chain Rule for Trigonometry
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Derivative of 1/x²
Power Rule with Negative Powers
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Derivative of cot(x)
Cotangent Derivative Rule
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Derivative of sec(x)
Secant Derivative Rule
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Derivative of csc(x)
Cosecant Derivative Rule
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Derivative of x⁴ - 4x³ + 6x² - 4x + 1
Polynomial Term-by-Term Differentiation
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Derivative of sin(3x)
Chain Rule for Trigonometric Functions
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Derivative of x · eˣ
Product Rule
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Derivative of x / (x + 1)
Quotient Rule
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Integrals with Steps (∫ dx)
Power rule, antiderivatives, u-substitution, and standard trigonometric integrals.
Integral of x dx
Power Rule for Integration
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Integral of x² dx
Power Rule for Integration
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Integral of x³ dx
Power Rule for Integration
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Integral of sin(x) dx
Sine Integration Rule
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Integral of cos(x) dx
Cosine Integration Rule
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Integral of eˣ dx
Exponential Integration Rule
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Integral of 1/x dx
Logarithmic Integration Rule
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Integral of √x dx
Power Rule with Fractional Exponents
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Integral of 1/x² dx
Power Rule for Negative Exponents
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Integral of (2x + 3) dx
Sum Rule for Integration
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Integral of (3x² - 4x + 1) dx
Polynomial Integration
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Integral of e^(2x) dx
Exponential Substitution
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Integral of cos(2x) dx
Linear Argument Integration
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Integral of sec²(x) dx
Secant Squared Integration
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Integral of (x + 1)² dx
Expansion & Power Rule
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Integral of x⁴ dx
Power Rule for Integration
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Integral of (4x³ - 3x² + 2x - 1) dx
Term-by-Term Polynomial Integration
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Integral of sin(2x) dx
Sine Substitution Rule
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Integral of sin(3x) dx
Trig u-Substitution
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Integral of (3x + 5) dx
Linear Term Integration
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Integral of 2/x dx
Constant Multiple with Natural Log
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Integral of (5x⁴ - 2x³ + 7) dx
Power Rule for Polynomials
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Quadratic & Polynomial Equations with Steps
Factoring, quadratic formula, difference of squares, repeated roots, and complex roots.
Solve x² - 5x + 6 = 0
Quadratic Formula & Factoring
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Solve x² - 4 = 0
Difference of Squares Identity
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Solve x² + 4x + 4 = 0
Perfect Square Trinomial
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Solve x² - 9 = 0
Difference of Two Squares
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Solve x² - 7x + 12 = 0
Factoring Trinomials
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Solve x² - 3x - 10 = 0
Factoring with Opposite Signs
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Solve x² - 2x - 8 = 0
Quadratic Formula & Factoring
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Solve 2x² + 5x - 3 = 0
Quadratic Formula with Leading Coefficient
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Solve 2x² - 7x + 3 = 0
Quadratic Formula
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Solve x² + 6x + 9 = 0
Perfect Square Trinomial
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Solve x² + 1 = 0
Complex Roots & Imaginary Unit
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Solve x² + 4 = 0
Imaginary Numbers Formula
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Solve x² - 6x + 8 = 0
Trinomial Factoring
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Solve x³ - x = 0
Common Factor & Difference of Squares
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Solve x³ - 6x² + 11x - 6 = 0
Rational Root Theorem & Synthetic Division
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Solve x² - 1 = 0
Difference of Squares
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Solve x² - 16 = 0
Difference of Squares
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Solve x² - 25 = 0
Difference of Squares
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Solve x² - 8x + 16 = 0
Perfect Square (x - k)²
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Solve 3x² + 10x + 3 = 0
Quadratic Formula with a = 3
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Solve x³ - 4x = 0
Greatest Common Factor & Difference of Squares
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