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Popular >

derivative of sin(xln(5x))

Solution

\frac{d}{d x} (sin (x) ln (5 x))

Solution

cos (x) ln (5 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (5 x))

Apply the Product Rule:

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

f = sin (x), g = ln (5 x)

= \frac{d}{d x} (sin (x)) ln (5 x) + \frac{d}{d x} (ln (5 x)) sin (x)

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= cos (x) ln (5 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (5 x) + \frac{sin ( x )}{x}

Popular Examples

derivative of e^{19}derivative of

e^{19}

(dy)/(dx)=e^4x+7y

\frac{d y}{d x} = e^{4} x + 7 y

integral of xsqrt(3x^2-6)

\int x 3 x^{2} - 6 d x

integral of 3/(5x^{2/5)}

\int \frac{3}{5 x ^{\frac{2}{5}}} d x

limit as x approaches 2 of (2x^2-5x+2)/(x^3-2x^2)

x \to 2 lim (\frac{2 x ^{2} - 5 x + 2}{x ^{3} - 2 x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(5x)) ?
The derivative of sin(xln(5x)) is cos(x)ln(5x)+(sin(x))/x
What is the first derivative of sin(xln(5x)) ?
The first derivative of sin(xln(5x)) is cos(x)ln(5x)+(sin(x))/x