What is the derivative of f(x)=cos^2(e^{cos^2(x)}) ?

The derivative of f(x)=cos^2(e^{cos^2(x)}) is e^{cos^2(x)}sin(2e^{cos^2(x)})sin(2x)

What is the first derivative of f(x)=cos^2(e^{cos^2(x)}) ?

The first derivative of f(x)=cos^2(e^{cos^2(x)}) is e^{cos^2(x)}sin(2e^{cos^2(x)})sin(2x)

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derivative of

f (x) = cos^{2} (e^{c o s^{2} (x)})

e^{c o s^{2} (x)} sin (2 e^{c o s^{2} (x)}) sin (2 x)

Solution steps

\frac{d}{d x} (cos^{2} (e^{c o s^{2} (x)}))

Apply the chain rule:

2 cos (e^{c o s^{2} (x)}) \frac{d}{d x} (cos (e^{c o s^{2} (x)}))

= 2 cos (e^{c o s^{2} (x)}) \frac{d}{d x} (cos (e^{c o s^{2} (x)}))

\frac{d}{d x} (cos (e^{c o s^{2} (x)})) = e^{c o s^{2} (x)} sin (e^{c o s^{2} (x)}) sin (2 x)

= 2 cos (e^{c o s^{2} (x)}) e^{c o s^{2} (x)} sin (e^{c o s^{2} (x)}) sin (2 x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= e^{c o s^{2} (x)} sin (2 e^{c o s^{2} (x)}) sin (2 x)

\int \frac{x ^{2} - 2 x - 4}{x ^{2} - 4 x} d x

\int_{- 1}^{1} (e^{x} - (x^{2} - 1)) d x

\int \frac{3 x + 1}{x ^{2} + 1} d x

\frac{\partial}{\partial y} (x y e^{- 1 y})

x \to 1 lim (sin (\frac{π x}{2}))

What is the derivative of f(x)=cos^2(e^{cos^2(x)}) ?
The derivative of f(x)=cos^2(e^{cos^2(x)}) is e^{cos^2(x)}sin(2e^{cos^2(x)})sin(2x)
What is the first derivative of f(x)=cos^2(e^{cos^2(x)}) ?
The first derivative of f(x)=cos^2(e^{cos^2(x)}) is e^{cos^2(x)}sin(2e^{cos^2(x)})sin(2x)