What is the derivative of y=4cos^4(x^2) ?

The derivative of y=4cos^4(x^2) is -32xcos^3(x^2)sin(x^2)

What is the first derivative of y=4cos^4(x^2) ?

The first derivative of y=4cos^4(x^2) is -32xcos^3(x^2)sin(x^2)

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derivative of

y = 4 cos^{4} (x^{2})

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

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

Simplify

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

n + 1

x + lo g_{10} (x) - 2

\frac{x}{( x ^{2} + 1 )}

\frac{d}{d s} (2 s)

y = sin (2 x - 4)

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