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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derivative of

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)

4 x^{3} + 6 x^{2} - x + 4

- 2 sin^{2} (x)

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

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

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

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)