Calculus Derivatives

Trig Derivatives

100

What is the derivative of y = sin(x) ?

y' = cos(x)

200

Find the derivative of f(x) = sec(x).

f'(x)=sec(x)tan(x)

300

Find the derivative of f(x) = 5-csc(x^2/2)

csc(x^2/2)cot(x^2/2)x

400

Find the derivative of f(x) = cos(tan(x))

-sin(tan(x))sec^2(x)

500

Find the derivative of y=(tan(2x))^1/2

y'= (sec^2(2x))/(tan(2x))^1/2

Product and Quotient Rule

100

Find the derivative of y = 3x² sin x

3x² cos x + 6x sin x

200

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

300

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

(-5x² + 4x + 5)/(x² + 1)²

400

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

500

Find f'(x) when f(x)= ((x+4)/((x^2+1)^1/2))^3

((x^2+1)^1/2-(x+4)(x^2+1)^-1/2(2x))/(x^2+1)

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

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

4 cos 4x

300

Find y' if y = (1+x^1/2)^1/2

(4x^1/2(1+x^1/2)^1/2))^-1

400

Find f''(x) if f(x) = (9x^2+4)^1/3

(6(-3x^2+4))/(9x^2+4)^5/3

Random

100

Find the derivative implicitly x² + y² = 30

y' = - x/y

200

sin x + 2cos 2y = 1

y' = cosx/4sin2y

300

(y - 2)² = 4x - 12

y' = 2/(y - 2)

400

x³ - 3x²y + 2xy² = 12

y' = (-3x² + 6xy - 2y²)/(-3x² + 4xy)