Calculus Derivatives

Exponential/Logarithmic Derivatives

100

Find the derivative of y = e^x

y' = e^x

200

Find the derivative of y = e^14x

y' = 14e^14x

300

Find the derivative of y = ln(3x⁵)

y' = 5/x

400

Find the derivative of f(x) = log₂(5x²)

f'(x) = 2/(x*ln(2))

500

Find the derivative of f(x) = 4log₇(3x⁸)

f'(x) = 32/(x*ln(7))

Product and Quotient Rule

100

Find the derivative of f(x) = (3x - 2x²)(5 + 4x)

f'(x) = -24x² + 4x + 15

200

Find the derivative of y = 3x² sin x

y' = 3x² cos(x) + 6x*sin(x)

300

Find the derivative of y = (5x - 2)/(x² + 1)

y' = (-5x² + 4x + 5)/(x² + 1)²

400

Find the derivative of y = 2x⁴(3x² - 1)

y' = 36x⁵ - 8x³

500

Find the derivative of f(x) = (2x + 5)/x⁴

f'(x) = (-6x⁴+5)/x⁸

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

Find the derivative of f(x) = sin(4x)

f'(x) = 4cos(4x)

300

Find the derivative of f(x) = -3(10x⁵ - 6x³)²

f'(x) = -6(10x⁵ - 6x³)(50x⁴ - 18x²)

400

f(x) = sin³(4x) Find f'(x)

f'(x) = 12sin²(4x) cos(4x)

500

Find y' if y = (9x² + 4)^1/3

y' = (6x)/(9x² + 4)^2/3

Implicit Differentiation

100

Find the derivative implicitly x² + y² = 30

dy/dx = - x/y

200

Find the derivative of 3x + 6y² = 7x

dy/dx = 1/(3y)

300

Find the derivative of (y - 2)² = 4x - 12

dy/dx = 2/(y - 2)

400

Find the derivative of 8x³ + 5y = 2x²

dy/dx = (24x²-4x)/-5

500

x³ - 3y + 2y² = 12

dy/dx = -3x²/(-3 + 4y)

Inverse Derivatives

100

Find (f-1)'(x) if f(x) = 2x - 12

(f-1)'(x) = 1/2

200

Find (f-1)'(x) if f(x) = -4x + 2

f-1)'(x) = -1/4

300

Find (f-1)'(x) of f(x) = sin-1(3x⁴)

(f'1)'(x) = 12x³/sqrt(1 - 9x⁸)

400

Find (f-1)'(x) when f(x) = cot-1(3x³)

(f-1)'(x) = -9x²/(1 + 9x⁶)

500

Find (f-1)'(x) if f(x) = x² - 4

f(-1)'(x) = 1/(2(x+4)^1/2)