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Popular >

derivative of f(x)=((4x)/(7x+5))^4

Solution

derivative of

f (x) = (\frac{4 x}{7 x + 5})^{4}

Solution

\frac{5120 x ^{3}}{( 7 x + 5 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{4 x}{7 x + 5})^{4})

Apply the chain rule:

4 (\frac{4 x}{7 x + 5})^{3} \frac{d}{d x} (\frac{4 x}{7 x + 5})

= 4 (\frac{4 x}{7 x + 5})^{3} \frac{d}{d x} (\frac{4 x}{7 x + 5})

\frac{d}{d x} (\frac{4 x}{7 x + 5}) = \frac{20}{( 7 x + 5 ) ^{2}}

= 4 (\frac{4 x}{7 x + 5})^{3} \frac{20}{( 7 x + 5 ) ^{2}}

Simplify

4 (\frac{4 x}{7 x + 5})^{3} \frac{20}{( 7 x + 5 ) ^{2}} : \frac{5120 x ^{3}}{( 7 x + 5 ) ^{5}}

= \frac{5120 x ^{3}}{( 7 x + 5 ) ^{5}}

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=((4x)/(7x+5))^4 ?
The derivative of f(x)=((4x)/(7x+5))^4 is (5120x^3)/((7x+5)^5)
What is the first derivative of f(x)=((4x)/(7x+5))^4 ?
The first derivative of f(x)=((4x)/(7x+5))^4 is (5120x^3)/((7x+5)^5)