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Popular >

derivative of sin(xln(9x))

Solution

\frac{d}{d x} (sin (x) ln (9 x))

Solution

cos (x) ln (9 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (9 x))

Apply the Product Rule:

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

f = sin (x), g = ln (9 x)

= \frac{d}{d x} (sin (x)) ln (9 x) + \frac{d}{d x} (ln (9 x)) sin (x)

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

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= cos (x) ln (9 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (9 x) + \frac{sin ( x )}{x}

Popular Examples

(\partial)/(\partial x)(e^{sin^2(x)})

\frac{\partial}{\partial x} (e^{s i n^{2} (x)})

integral from 0 to 1 of 3^{3x}

\int_{0}^{1} 3^{3 x} d x

derivative of 1/(y^2)-5/(y^4)(y+9y^3)derivative of

\frac{1}{y ^{2}} - \frac{5}{y ^{4}} (y + 9 y^{3})

(\partial)/(\partial x)(sin(xy^3))

\frac{\partial}{\partial x} (sin (x y^{3}))

integral of x^3(5+x^4)^5

\int x^{3} (5 + x^{4})^{5} d x

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(9x)) ?
The derivative of sin(xln(9x)) is cos(x)ln(9x)+(sin(x))/x
What is the first derivative of sin(xln(9x)) ?
The first derivative of sin(xln(9x)) is cos(x)ln(9x)+(sin(x))/x