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

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

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

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

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derivative of

3^{s i n (x)}

ln (3) \cdot 3^{s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (3^{s i n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{s i n (x) l n (3)} \frac{d}{d x} (sin (x) ln (3))

= e^{s i n (x) l n (3)} \frac{d}{d x} (sin (x) ln (3))

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

= e^{s i n (x) l n (3)} ln (3) cos (x)

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

= ln (3) \cdot 3^{s i n (x)} cos (x)

\int \frac{1}{8} e^{8 x} d x

\frac{d}{d x} (9 (2 x e^{x} + e^{x} x^{2}))

\int_{1}^{4} \frac{5}{x} d x

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

\frac{d y}{d x} - \frac{2 y}{x} = x^{2} sin (3 x)

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