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Popular >

derivative of sin(x)ln(6x)

Solution

derivative of

sin (x) ln (6 x)

Solution

cos (x) ln (6 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (6 x))

Apply the Product Rule:

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

f = sin (x), g = ln (6 x)

= \frac{d}{d x} (sin (x)) ln (6 x) + \frac{d}{d x} (ln (6 x)) sin (x)

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

\frac{d}{d x} (ln (6 x)) = \frac{1}{x}

= cos (x) ln (6 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (6 x) + \frac{sin ( x )}{x}

Popular Examples

(\partial)/(\partial t)(2/((x-3t)^2+1))

\frac{\partial}{\partial t} (\frac{2}{( x - 3 t ) ^{2} + 1})

(\partial)/(\partial x)(x^6y^8+7x^7y)

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{7} y)

integral of x^2sin(x^3+4)

\int x^{2} sin (x^{3} + 4) d x

limit as x approaches c of x

x \to c lim (x)

(\partial)/(\partial x)(xy^2-x^2y)

\frac{\partial}{\partial x} (x y^{2} - x^{2} y)

Frequently Asked Questions (FAQ)

What is the derivative of sin(x)ln(6x) ?
The derivative of sin(x)ln(6x) is cos(x)ln(6x)+(sin(x))/x
What is the first derivative of sin(x)ln(6x) ?
The first derivative of sin(x)ln(6x) is cos(x)ln(6x)+(sin(x))/x