What is the derivative of 3^{cos(x}) ?

The derivative of 3^{cos(x}) is -ln(3)*3^{cos(x)}sin(x)

What is the first derivative of 3^{cos(x}) ?

The first derivative of 3^{cos(x}) is -ln(3)*3^{cos(x)}sin(x)

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Popular >

\frac{d}{d x} (3^{c o s (x)})

- ln (3) \cdot 3^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (3^{c o s (x)})

Apply exponent rule:

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

3^{c o s (x)} = e^{c o s (x) l n (3)}

= \frac{d}{d x} (e^{c o s (x) l n (3)})

Apply the chain rule:

e^{c o s (x) l n (3)} \frac{d}{d x} (cos (x) ln (3))

= e^{c o s (x) l n (3)} \frac{d}{d x} (cos (x) ln (3))

\frac{d}{d x} (cos (x) ln (3)) = - ln (3) sin (x)

= e^{c o s (x) l n (3)} (- ln (3) sin (x))

Simplify

e^{c o s (x) l n (3)} (- ln (3) sin (x)) : - ln (3) \cdot 3^{c o s (x)} sin (x)

= - ln (3) \cdot 3^{c o s (x)} sin (x)

\int \frac{5}{7 + 5 x} d x

\frac{d}{d x} (x^{2} + A x + B)

\int 2 tan^{3} (\frac{x}{4}) d x

n \to \infty lim ((1 + \frac{3}{n})^{- n^{2}})

\int 4 x e^{4 x} d x

What is the derivative of 3^{cos(x}) ?
The derivative of 3^{cos(x}) is -ln(3)*3^{cos(x)}sin(x)
What is the first derivative of 3^{cos(x}) ?
The first derivative of 3^{cos(x}) is -ln(3)*3^{cos(x)}sin(x)