What is the derivative of sin(x)ln(8x) ?

The derivative of sin(x)ln(8x) is cos(x)ln(8x)+(sin(x))/x

What is the first derivative of sin(x)ln(8x) ?

The first derivative of sin(x)ln(8x) is cos(x)ln(8x)+(sin(x))/x

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derivative of

sin (x) ln (8 x)

cos (x) ln (8 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (8 x))

Apply the Product Rule:

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

f = sin (x), g = ln (8 x)

= \frac{d}{d x} (sin (x)) ln (8 x) + \frac{d}{d x} (ln (8 x)) sin (x)

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

\frac{d}{d x} (ln (8 x)) = \frac{1}{x}

= cos (x) ln (8 x) + \frac{1}{x} sin (x)

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= cos (x) ln (8 x) + \frac{sin ( x )}{x}

\frac{d}{d x} (e^{x} + 4)

\int_{- 3}^{3} (9 - x^{2})^{2} d x

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

\int e^{x} + x^{2} d x

x \to 0 lim (0)

What is the derivative of sin(x)ln(8x) ?
The derivative of sin(x)ln(8x) is cos(x)ln(8x)+(sin(x))/x
What is the first derivative of sin(x)ln(8x) ?
The first derivative of sin(x)ln(8x) is cos(x)ln(8x)+(sin(x))/x