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

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

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

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

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derivative of

f (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)

\int \frac{2 + w ^{4}}{w ^{3} + 9 w} d w

\frac{d y}{d x} + \frac{y}{x} = \frac{1}{x}

sin^{3} (4 x)

y^{^{'}} - 5 y = 0

\frac{d}{d x} (\frac{1}{( 1 - 2500 x ) ^{4}})

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