What is the derivative of f(x)=ln(2x^5(5x-1)^3) ?

The derivative of f(x)=ln(2x^5(5x-1)^3) is (5(8x-1))/(x(5x-1))

What is the first derivative of f(x)=ln(2x^5(5x-1)^3) ?

The first derivative of f(x)=ln(2x^5(5x-1)^3) is (5(8x-1))/(x(5x-1))

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derivative of

f (x) = ln (2 x^{5} (5 x - 1)^{3})

\frac{5 ( 8 x - 1 )}{x ( 5 x - 1 )}

Solution steps

\frac{d}{d x} (ln (2 x^{5} (5 x - 1)^{3}))

Apply the chain rule:

\frac{1}{2 x ^{5} ( 5 x - 1 ) ^{3}} \frac{d}{d x} (2 x^{5} (5 x - 1)^{3})

= \frac{1}{2 x ^{5} ( 5 x - 1 ) ^{3}} \frac{d}{d x} (2 x^{5} (5 x - 1)^{3})

\frac{d}{d x} (2 x^{5} (5 x - 1)^{3}) = 2 (5 x^{4} (5 x - 1)^{3} + 15 (5 x - 1)^{2} x^{5})

= \frac{1}{2 x ^{5} ( 5 x - 1 ) ^{3}} \cdot 2 (5 x^{4} (5 x - 1)^{3} + 15 (5 x - 1)^{2} x^{5})

Simplify

\frac{1}{2 x ^{5} ( 5 x - 1 ) ^{3}} \cdot 2 (5 x^{4} (5 x - 1)^{3} + 15 (5 x - 1)^{2} x^{5}) : \frac{5 ( 8 x - 1 )}{x ( 5 x - 1 )}

= \frac{5 ( 8 x - 1 )}{x ( 5 x - 1 )}

y = 3 x + 1

\frac{d}{d x} ((9 x^{6} + 4 x^{3})^{4})

t \to π lim (sin (\frac{3}{4} t))

(ln (x))^{5 c o s (x)}

(- 4, 7), (2, - 8)

What is the derivative of f(x)=ln(2x^5(5x-1)^3) ?
The derivative of f(x)=ln(2x^5(5x-1)^3) is (5(8x-1))/(x(5x-1))
What is the first derivative of f(x)=ln(2x^5(5x-1)^3) ?
The first derivative of f(x)=ln(2x^5(5x-1)^3) is (5(8x-1))/(x(5x-1))