What is the derivative of 1/(4x^3+5x^2-7x+8) ?

The derivative of 1/(4x^3+5x^2-7x+8) is -(12x^2+10x-7)/((4x^3+5x^2-7x+8)^2)

What is the first derivative of 1/(4x^3+5x^2-7x+8) ?

The first derivative of 1/(4x^3+5x^2-7x+8) is -(12x^2+10x-7)/((4x^3+5x^2-7x+8)^2)

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\frac{d}{d x} (\frac{1}{4 x ^{3} + 5 x ^{2} - 7 x + 8})

- \frac{12 x ^{2} + 10 x - 7}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{4 x ^{3} + 5 x ^{2} - 7 x + 8})

Apply exponent rule:

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

= \frac{d}{d x} ((4 x^{3} + 5 x^{2} - 7 x + 8)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}} \frac{d}{d x} (4 x^{3} + 5 x^{2} - 7 x + 8)

= - \frac{1}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}} \frac{d}{d x} (4 x^{3} + 5 x^{2} - 7 x + 8)

\frac{d}{d x} (4 x^{3} + 5 x^{2} - 7 x + 8) = 12 x^{2} + 10 x - 7

= - \frac{1}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}} (12 x^{2} + 10 x - 7)

Simplify

- \frac{1}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}} (12 x^{2} + 10 x - 7) : - \frac{12 x ^{2} + 10 x - 7}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}}

= - \frac{12 x ^{2} + 10 x - 7}{( 4 x ^{3} + 5 x ^{2} - 7 x + 8 ) ^{2}}

\int x (x^{2} + 3)^{7} d x

\frac{d}{d x} (x^{2} e n (x))

y = tan (3 x)

\int \frac{1}{( x - 7 ) ^{2}} - 1 d x

n = 1 \sum \infty \frac{1}{2 n}

What is the derivative of 1/(4x^3+5x^2-7x+8) ?
The derivative of 1/(4x^3+5x^2-7x+8) is -(12x^2+10x-7)/((4x^3+5x^2-7x+8)^2)
What is the first derivative of 1/(4x^3+5x^2-7x+8) ?
The first derivative of 1/(4x^3+5x^2-7x+8) is -(12x^2+10x-7)/((4x^3+5x^2-7x+8)^2)