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

The derivative of (4x^2+1)/(x^2+5) is (38x)/((x^2+5)^2)

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

The first derivative of (4x^2+1)/(x^2+5) is (38x)/((x^2+5)^2)

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derivative of

\frac{4 x ^{2} + 1}{x ^{2} + 5}

\frac{38 x}{( x ^{2} + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Expand

8 x (x^{2} + 5) - 2 x (4 x^{2} + 1) : 38 x

= \frac{38 x}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (x^{4} - 6 x^{2} + 4)

x e^{\frac{1}{x}}

\frac{d}{d x} (1 + 4 x^{\frac{3}{2}})

\int \frac{d ^{2} w}{2} d x

f (t) = ln (t + 1)

What is the derivative of (4x^2+1)/(x^2+5) ?
The derivative of (4x^2+1)/(x^2+5) is (38x)/((x^2+5)^2)
What is the first derivative of (4x^2+1)/(x^2+5) ?
The first derivative of (4x^2+1)/(x^2+5) is (38x)/((x^2+5)^2)