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

The derivative of 4^{cos(x}) is -ln(2)*2^{2cos(x)+1}sin(x)

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

The first derivative of 4^{cos(x}) is -ln(2)*2^{2cos(x)+1}sin(x)

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

- ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

4^{c o s (x)} = e^{c o s (x) l n (4)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (cos (x) ln (4)) = - 2 ln (2) sin (x)

= e^{c o s (x) l n (4)} (- 2 ln (2) sin (x))

Simplify

e^{c o s (x) l n (4)} (- 2 ln (2) sin (x)) : - ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

= - ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

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

x \to - 5 lim (\frac{x - 5}{x + 5})

x^{2}, 9

x y^{^{'}} + y = 50 x

f (x) = \frac{8 x}{e ^{x}}

What is the derivative of 4^{cos(x}) ?
The derivative of 4^{cos(x}) is -ln(2)*2^{2cos(x)+1}sin(x)
What is the first derivative of 4^{cos(x}) ?
The first derivative of 4^{cos(x}) is -ln(2)*2^{2cos(x)+1}sin(x)