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Popular >

derivative of 1/((4x+5^2))

Solution

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

Solution

- \frac{8}{( 4 x + 5 ) ^{3}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{8}{( 4 x + 5 ) ^{3}}

Popular Examples

integral of (xln(x^2+4))/(x^2+4)

\int \frac{x ln ( x ^{2} + 4 )}{x ^{2} + 4} d x

integral of x^2sqrt(x^3+37)

\int x^{2} x^{3} + 37 d x

integral of (x+2)/(x-1)

\int \frac{x + 2}{x - 1} d x

tangent of f(x)=sqrt(7x+2),\at x=2 tangent of

f (x) = 7 x + 2, at x = 2

slope of (0,1),(5,4)slope

(0, 1), (5, 4)

Frequently Asked Questions (FAQ)

What is the derivative of 1/((4x+5^2)) ?
The derivative of 1/((4x+5^2)) is -8/((4x+5)^3)
What is the first derivative of 1/((4x+5^2)) ?
The first derivative of 1/((4x+5^2)) is -8/((4x+5)^3)