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

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

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

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

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derivative of

e^{3 x} \cdot sin (ln (x))

3 e^{3 x} sin (ln (x)) + \frac{e ^{3 x} cos ( ln ( x ) )}{x}

Solution steps

\frac{d}{d x} (e^{3 x} sin (ln (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{3 x}, g = sin (ln (x))

= \frac{d}{d x} (e^{3 x}) sin (ln (x)) + \frac{d}{d x} (sin (ln (x))) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

= e^{3 x} \cdot 3 sin (ln (x)) + \frac{cos ( ln ( x ) )}{x} e^{3 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 3 e^{3 x} sin (ln (x)) + \frac{e ^{3 x} cos ( ln ( x ) )}{x}

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