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Popular >

derivative of x^9ln(7x)

Solution

\frac{d}{d x} (x^{9} ln (7 x))

Solution

9 x^{8} ln (7 x) + x^{8}

Solution steps

\frac{d}{d x} (x^{9} ln (7 x))

Apply the Product Rule:

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

f = x^{9}, g = ln (7 x)

= \frac{d}{d x} (x^{9}) ln (7 x) + \frac{d}{d x} (ln (7 x)) x^{9}

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

= 9 x^{8} ln (7 x) + \frac{1}{x} x^{9}

\frac{1}{x} x^{9} = x^{8}

= 9 x^{8} ln (7 x) + x^{8}

Popular Examples

sum from n=1 to infinity of 1/(4n^2+5)

n = 1 \sum \infty \frac{1}{4 n ^{2} + 5}

derivative of (5-sec(x)/(tan(x)))

\frac{d}{d x} (\frac{5 - sec ( x )}{tan ( x )})

derivative of y=9 derivative of

y = 9

tangent of f(x)=(sqrt(x)+1)/(sqrt(x)+3)tangent of

f (x) = \frac{x + 1}{x + 3}

limit as x approaches 0-of 1/(x^3-2x^2)

x \to 0 - lim (\frac{1}{x ^{3} - 2 x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of x^9ln(7x) ?
The derivative of x^9ln(7x) is 9x^8ln(7x)+x^8
What is the first derivative of x^9ln(7x) ?
The first derivative of x^9ln(7x) is 9x^8ln(7x)+x^8