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Popular >

derivative of sin(xln(7x))

Solution

\frac{d}{d x} (sin (x) ln (7 x))

Solution

cos (x) ln (7 x) + \frac{sin ( x )}{x}

Solution steps

\frac{d}{d x} (sin (x) ln (7 x))

Apply the Product Rule:

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

f = sin (x), g = ln (7 x)

= \frac{d}{d x} (sin (x)) ln (7 x) + \frac{d}{d x} (ln (7 x)) sin (x)

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

\frac{d}{d x} (ln (7 x)) = \frac{1}{x}

= cos (x) ln (7 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (7 x) + \frac{sin ( x )}{x}

Popular Examples

integral of (3u^5-2u^3)

\int (3 u^{5} - 2 u^{3}) d u

area f(x)=x+3,0,5 area

f (x) = x + 3, 0, 5

limit as x approaches infinity of (x^{100}+1/(x^3))/(pi-x^{97)}

x \to \infty lim (\frac{x ^{100} + \frac{1}{x ^{3}}}{π - x ^{97}})

(\partial)/(\partial x)(e^{xyz^2+z})

\frac{\partial}{\partial x} (e^{x y z^{2} + z})

y^{^{''}} + 196 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of sin(xln(7x)) ?
The derivative of sin(xln(7x)) is cos(x)ln(7x)+(sin(x))/x
What is the first derivative of sin(xln(7x)) ?
The first derivative of sin(xln(7x)) is cos(x)ln(7x)+(sin(x))/x