What is the derivative of h(x)= 1/(x^2+4x-21) ?

The derivative of h(x)= 1/(x^2+4x-21) is -(2x+4)/((x^2+4x-21)^2)

What is the first derivative of h(x)= 1/(x^2+4x-21) ?

The first derivative of h(x)= 1/(x^2+4x-21) is -(2x+4)/((x^2+4x-21)^2)

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derivative of

h (x) = \frac{1}{x ^{2} + 4 x - 21}

- \frac{2 x + 4}{( x ^{2} + 4 x - 21 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{2} + 4 x - 21})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{2} + 4 x - 21)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{2} + 4 x - 21 ) ^{2}} \frac{d}{d x} (x^{2} + 4 x - 21)

= - \frac{1}{( x ^{2} + 4 x - 21 ) ^{2}} \frac{d}{d x} (x^{2} + 4 x - 21)

\frac{d}{d x} (x^{2} + 4 x - 21) = 2 x + 4

= - \frac{1}{( x ^{2} + 4 x - 21 ) ^{2}} (2 x + 4)

Simplify

- \frac{1}{( x ^{2} + 4 x - 21 ) ^{2}} (2 x + 4) : - \frac{2 x + 4}{( x ^{2} + 4 x - 21 ) ^{2}}

= - \frac{2 x + 4}{( x ^{2} + 4 x - 21 ) ^{2}}

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\frac{d}{d x} (e^{x^{3} + 8 x})

What is the derivative of h(x)= 1/(x^2+4x-21) ?
The derivative of h(x)= 1/(x^2+4x-21) is -(2x+4)/((x^2+4x-21)^2)
What is the first derivative of h(x)= 1/(x^2+4x-21) ?
The first derivative of h(x)= 1/(x^2+4x-21) is -(2x+4)/((x^2+4x-21)^2)