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

The derivative of (4x^2+5/(x^2+7)) is (46x)/((x^2+7)^2)

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

The first derivative of (4x^2+5/(x^2+7)) is (46x)/((x^2+7)^2)

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\frac{d}{d x} (\frac{4 x ^{2} + 5}{x ^{2} + 7})

\frac{46 x}{( x ^{2} + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} + 5}{x ^{2} + 7})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{2} + 7) = 2 x

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

Expand

8 x (x^{2} + 7) - 2 x (4 x^{2} + 5) : 46 x

= \frac{46 x}{( x ^{2} + 7 ) ^{2}}

\frac{\partial}{\partial y} (10 - 6 y + e^{- 3 x})

\frac{d}{d t} (3 e^{t})

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

\frac{d y}{d x} = y + y^{3}

\int_{- 9}^{4} ∣ x + 5 ∣ d x

What is the derivative of (4x^2+5/(x^2+7)) ?
The derivative of (4x^2+5/(x^2+7)) is (46x)/((x^2+7)^2)
What is the first derivative of (4x^2+5/(x^2+7)) ?
The first derivative of (4x^2+5/(x^2+7)) is (46x)/((x^2+7)^2)