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Popular >

derivative of f(x)=ln^3(sqrt(3x-5))

Solution

derivative of

f (x) = ln^{3} (3 x - 5)

Solution

\frac{9 ln ^{2} ( 3 x - 5 )}{2 ( 3 x - 5 )}

Solution steps

\frac{d}{d x} (ln^{3} (3 x - 5))

Apply the chain rule:

3 (ln (3 x - 5))^{2} \frac{d}{d x} (ln (3 x - 5))

= 3 (ln (3 x - 5))^{2} \frac{d}{d x} (ln (3 x - 5))

\frac{d}{d x} (ln (3 x - 5)) = \frac{3}{2 ( 3 x - 5 )}

= 3 (ln (3 x - 5))^{2} \frac{3}{2 ( 3 x - 5 )}

Simplify

3 ln^{2} (3 x - 5) \frac{3}{2 ( 3 x - 5 )} : \frac{9 ln ^{2} ( 3 x - 5 )}{2 ( 3 x - 5 )}

= \frac{9 ln ^{2} ( 3 x - 5 )}{2 ( 3 x - 5 )}

Popular Examples

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\int sec^{2} (t) + t (t^{2} + 1)^{3} + t^{2} ln (t) d t

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\frac{d}{d x} (e^{s i n (3 x)})

y^{^{'}} - 2 y = 2 - 4 x

(\partial)/(\partial x)((-18x)/((x-y)^4))

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln^3(sqrt(3x-5)) ?
The derivative of f(x)=ln^3(sqrt(3x-5)) is (9ln^2(sqrt(3x-5)))/(2(3x-5))
What is the first derivative of f(x)=ln^3(sqrt(3x-5)) ?
The first derivative of f(x)=ln^3(sqrt(3x-5)) is (9ln^2(sqrt(3x-5)))/(2(3x-5))