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

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

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

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

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derivative of

y = 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{x ^{3}}{x ^{4} + 9} d x

\int_{- 1}^{5} (∣ x - 2 ∣) d x

f (x) = 9^{x} + e^{x}

x^{3}, - 2

tan (x)

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