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Popular >

derivative of 1/((x+9^2))

Solution

\frac{d}{d x} (\frac{1}{( x + 9 ) ^{2}})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{( x + 9 ) ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((x + 9)^{- 2})

Apply the chain rule:

- \frac{2}{( x + 9 ) ^{3}} \frac{d}{d x} (x + 9)

= - \frac{2}{( x + 9 ) ^{3}} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = 1

= - \frac{2}{( x + 9 ) ^{3}} \cdot 1

Simplify

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

Popular Examples

(\partial)/(\partial x)((-x^4+7y^2+3y)^6)

\frac{\partial}{\partial x} ((- x^{4} + 7 y^{2} + 3 y)^{6})

integral of 1+1/(2x)

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

y^{''}-5y^'+4y=0,y(0)=3,y^'(0)=2

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 2

integral from 1 to 3 of e^x

\int_{1}^{3} e^{x} d x

derivative of 18+(12)/((0.0004x^2+1)^2)derivative of

18 + \frac{12}{( 0.0004 x ^{2} + 1 ) ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of 1/((x+9^2)) ?
The derivative of 1/((x+9^2)) is -2/((x+9)^3)
What is the first derivative of 1/((x+9^2)) ?
The first derivative of 1/((x+9^2)) is -2/((x+9)^3)