What is the derivative of 1/((x^3+9^5)) ?

The derivative of 1/((x^3+9^5)) is -(15x^2)/((x^3+9)^6)

What is the first derivative of 1/((x^3+9^5)) ?

The first derivative of 1/((x^3+9^5)) is -(15x^2)/((x^3+9)^6)

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\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

- \frac{15 x ^{2}}{( x ^{3} + 9 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{3} + 9)^{- 5})

Apply the chain rule:

- \frac{5}{( x ^{3} + 9 ) ^{6}} \frac{d}{d x} (x^{3} + 9)

= - \frac{5}{( x ^{3} + 9 ) ^{6}} \frac{d}{d x} (x^{3} + 9)

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

= - \frac{5}{( x ^{3} + 9 ) ^{6}} \cdot 3 x^{2}

Simplify

- \frac{5}{( x ^{3} + 9 ) ^{6}} \cdot 3 x^{2} : - \frac{15 x ^{2}}{( x ^{3} + 9 ) ^{6}}

= - \frac{15 x ^{2}}{( x ^{3} + 9 ) ^{6}}

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

x^{2} - 1

\frac{\partial}{\partial x} (- x y^{2} + x y)

\frac{d}{d x} (\frac{x}{x - 1})

x^{2} y^{^{'}} + 2 x y = 5 y^{4}

What is the derivative of 1/((x^3+9^5)) ?
The derivative of 1/((x^3+9^5)) is -(15x^2)/((x^3+9)^6)
What is the first derivative of 1/((x^3+9^5)) ?
The first derivative of 1/((x^3+9^5)) is -(15x^2)/((x^3+9)^6)