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

The derivative of cos^2(x^2) is -4xcos(x^2)sin(x^2)

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

The first derivative of cos^2(x^2) is -4xcos(x^2)sin(x^2)

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

- 4 x cos (x^{2}) sin (x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{9 ^{x} - 1 5 ^{- x}}{x})

(6.3) (4.2)

\int t^{2} - 1 d t

\int \frac{3}{5} - \frac{7}{x} d x

\int \frac{1}{x ^{1.00001}} d x

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