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

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

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

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

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derivative of

\frac{1}{5 x ^{2} + 3 x}

- \frac{10 x + 3}{( 5 x ^{2} + 3 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{5 x ^{2} + 3 x})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2} + 3 x) = 10 x + 3

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

Simplify

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

= - \frac{10 x + 3}{( 5 x ^{2} + 3 x ) ^{2}}

10 y^{^{''}} + 1000 y = 130 cos (8 t)

\frac{3}{( s - 3 ) ^{3}}

\int e^{2 x} (1 - 5 e^{2 x})^{2} d x

\frac{\partial}{\partial x} (e^{- 2 x^{2} - 3 y^{2}})

\int 9 x^{3} (x^{3} + 2 x^{2} + x + 8) d x

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