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

The derivative of 3/((2x^2+5)^2) is -(24x)/((2x^2+5)^3)

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

The first derivative of 3/((2x^2+5)^2) is -(24x)/((2x^2+5)^3)

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derivative of

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

- \frac{24 x}{( 2 x ^{2} + 5 ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= 3 (- \frac{2}{( 2 x ^{2} + 5 ) ^{3}} \cdot 4 x)

Simplify

3 (- \frac{2}{( 2 x ^{2} + 5 ) ^{3}} \cdot 4 x) : - \frac{24 x}{( 2 x ^{2} + 5 ) ^{3}}

= - \frac{24 x}{( 2 x ^{2} + 5 ) ^{3}}

2 - x^{2}

y = lo g_{4} (x^{2})

cos (x - 2 5^{\circ})

f (x) = [x - \frac{1}{x}]^{2}

(x^{\frac{1}{2}})^{2}

What is the derivative of 3/((2x^2+5)^2) ?
The derivative of 3/((2x^2+5)^2) is -(24x)/((2x^2+5)^3)
What is the first derivative of 3/((2x^2+5)^2) ?
The first derivative of 3/((2x^2+5)^2) is -(24x)/((2x^2+5)^3)