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Popular >

derivative of (3x^2-9^{-15})

Solution

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

Solution

- \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

Solution steps

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

Apply the chain rule:

- \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \frac{d}{d x} (3 x^{2} - 9)

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

= - \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \cdot 6 x

Simplify

- \frac{15}{( 3 x ^{2} - 9 ) ^{16}} \cdot 6 x : - \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

= - \frac{10 x}{4782969 ( x ^{2} - 3 ) ^{16}}

Popular Examples

tangent of y=(x^2-2)(x^3-3x),(-2,-4)tangent of

y = (x^{2} - 2) (x^{3} - 3 x), (- 2, - 4)

derivative of 3x^2-4x+2

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

tangent of y=x^2-3x+3,(4,7)tangent of

y = x^{2} - 3 x + 3, (4, 7)

(d^2)/(dx^2)(sqrt(4x+1))

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

integral of 2x+5e^x

\int 2 x + 5 e^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-9^{-15}) ?
The derivative of (3x^2-9^{-15}) is -(10x)/(4782969(x^2-3)^{16)}
What is the first derivative of (3x^2-9^{-15}) ?
The first derivative of (3x^2-9^{-15}) is -(10x)/(4782969(x^2-3)^{16)}