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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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x \to 1 lim (2 x^{2} + 3 x + 1)

\int_{5}^{9} \frac{x}{x ^{2} - 10 x + 41} d x

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