What is the derivative of f(x)= 1/(4x^2+5x) ?

The derivative of f(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)

What is the first derivative of f(x)= 1/(4x^2+5x) ?

The first derivative of f(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)

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derivative of

f (x) = \frac{1}{4 x ^{2} + 5 x}

- \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{4 x ^{2} + 5 x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{2} + 5 x) = 8 x + 5

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

Simplify

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

= - \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

\frac{925 + 20 x - 0.079 x ^{2}}{484}

\frac{d}{d x} (\frac{csc ^{2} ( x ) - cot ^{3} ( x )}{tan ( x ^{2} + 2 x )})

\int x \cdot lo g_{e} (x) d x

\int_{9}^{24} (- x + 12) d x

ln (s)

What is the derivative of f(x)= 1/(4x^2+5x) ?
The derivative of f(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)
What is the first derivative of f(x)= 1/(4x^2+5x) ?
The first derivative of f(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)