What is the derivative of ((3x-1/(5x+2))^4) ?

The derivative of ((3x-1/(5x+2))^4) is (44(3x-1)^3)/((5x+2)^5)

What is the first derivative of ((3x-1/(5x+2))^4) ?

The first derivative of ((3x-1/(5x+2))^4) is (44(3x-1)^3)/((5x+2)^5)

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

\frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 x - 1}{5 x + 2}) = \frac{11}{( 5 x + 2 ) ^{2}}

= 4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{11}{( 5 x + 2 ) ^{2}}

Simplify

4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{11}{( 5 x + 2 ) ^{2}} : \frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

= \frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

\int_{- 1}^{4} (\frac{x}{5 + x}) d x

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

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What is the derivative of ((3x-1/(5x+2))^4) ?
The derivative of ((3x-1/(5x+2))^4) is (44(3x-1)^3)/((5x+2)^5)
What is the first derivative of ((3x-1/(5x+2))^4) ?
The first derivative of ((3x-1/(5x+2))^4) is (44(3x-1)^3)/((5x+2)^5)