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

The derivative of 3^{sin(3x}) is ln(3)*3^{sin(3x)+1}cos(3x)

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

The first derivative of 3^{sin(3x}) is ln(3)*3^{sin(3x)+1}cos(3x)

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

ln (3) \cdot 3^{s i n (3 x) + 1} cos (3 x)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{s i n (3 x) l n (3)} ln (3) cos (3 x) \cdot 3 : ln (3) \cdot 3^{s i n (3 x) + 1} cos (3 x)

= ln (3) \cdot 3^{s i n (3 x) + 1} cos (3 x)

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e (t + 1)

\frac{\partial}{\partial y} (3 x^{4} e^{y})

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What is the derivative of 3^{sin(3x}) ?
The derivative of 3^{sin(3x}) is ln(3)*3^{sin(3x)+1}cos(3x)
What is the first derivative of 3^{sin(3x}) ?
The first derivative of 3^{sin(3x}) is ln(3)*3^{sin(3x)+1}cos(3x)