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Popular >

derivative of cos^4(4x^2+1)

Solution

\frac{d}{d x} (cos^{4} (4 x^{2} + 1))

Solution

- 32 x cos^{3} (4 x^{2} + 1) sin (4 x^{2} + 1)

Solution steps

\frac{d}{d x} (cos^{4} (4 x^{2} + 1))

Apply the chain rule:

4 (cos (4 x^{2} + 1))^{3} \frac{d}{d x} (cos (4 x^{2} + 1))

= 4 (cos (4 x^{2} + 1))^{3} \frac{d}{d x} (cos (4 x^{2} + 1))

\frac{d}{d x} (cos (4 x^{2} + 1)) = - sin (4 x^{2} + 1) \cdot 8 x

= 4 (cos (4 x^{2} + 1))^{3} (- sin (4 x^{2} + 1) \cdot 8 x)

Simplify

= - 32 x cos^{3} (4 x^{2} + 1) sin (4 x^{2} + 1)

Popular Examples

integral of (3x^2+4x-6)

\int (3 x^{2} + 4 x - 6) d x

derivative of-1/3 (x^{-3}-x^6)

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

derivative of sqrt(33+4t)derivative of

33 + 4 t

derivative of (x^2)/((4+x))derivative of

\frac{x ^{2}}{( 4 + x )}

integral of 1/(1+cos(θ))

\int \frac{1}{1 + cos ( θ )} d θ

Frequently Asked Questions (FAQ)

What is the derivative of cos^4(4x^2+1) ?
The derivative of cos^4(4x^2+1) is -32xcos^3(4x^2+1)sin(4x^2+1)
What is the first derivative of cos^4(4x^2+1) ?
The first derivative of cos^4(4x^2+1) is -32xcos^3(4x^2+1)sin(4x^2+1)