What is the derivative of e^{cos(4x}) ?

The derivative of e^{cos(4x}) is -4e^{cos(4x)}sin(4x)

What is the first derivative of e^{cos(4x}) ?

The first derivative of e^{cos(4x}) is -4e^{cos(4x)}sin(4x)

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\frac{d}{d x} (e^{c o s (4 x)})

- 4 e^{c o s (4 x)} sin (4 x)

Solution steps

\frac{d}{d x} (e^{c o s (4 x)})

Apply the chain rule:

e^{c o s (4 x)} \frac{d}{d x} (cos (4 x))

= e^{c o s (4 x)} \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= e^{c o s (4 x)} (- sin (4 x) \cdot 4)

Simplify

= - 4 e^{c o s (4 x)} sin (4 x)

(6.3) (7.8)

33 x^{3}

\int \frac{a + b x ^{7}}{8 a x + b x ^{8}} d x

f (x) = 4 e^{x} + x, at x = 0

\frac{d}{d x} (cos (\frac{1 - e ^{7 x}}{1 + e ^{7 x}}))

What is the derivative of e^{cos(4x}) ?
The derivative of e^{cos(4x}) is -4e^{cos(4x)}sin(4x)
What is the first derivative of e^{cos(4x}) ?
The first derivative of e^{cos(4x}) is -4e^{cos(4x)}sin(4x)