What is the derivative of (3x^2/(5x^2+7x)) ?

The derivative of (3x^2/(5x^2+7x)) is (21)/((5x+7)^2)

What is the first derivative of (3x^2/(5x^2+7x)) ?

The first derivative of (3x^2/(5x^2+7x)) is (21)/((5x+7)^2)

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\frac{d}{d x} (\frac{3 x ^{2}}{5 x ^{2} + 7 x})

\frac{21}{( 5 x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2}}{5 x ^{2} + 7 x})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x ^{2}}{5 x ^{2} + 7 x})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 5 x ^{2} + 7 x ) - \frac{d}{d x} ( 5 x ^{2} + 7 x ) x ^{2}}{( 5 x ^{2} + 7 x ) ^{2}}

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

\frac{d}{d x} (5 x^{2} + 7 x) = 10 x + 7

= 3 \cdot \frac{2 x ( 5 x ^{2} + 7 x ) - ( 10 x + 7 ) x ^{2}}{( 5 x ^{2} + 7 x ) ^{2}}

Simplify

3 \cdot \frac{2 x ( 5 x ^{2} + 7 x ) - ( 10 x + 7 ) x ^{2}}{( 5 x ^{2} + 7 x ) ^{2}} : \frac{21}{( 5 x + 7 ) ^{2}}

= \frac{21}{( 5 x + 7 ) ^{2}}

5 cos (x)

\frac{\partial}{\partial x} (x ln (t))

e^{x} - e^{- x}

\int sin (x) \cdot x d x

\frac{d}{d x} (cos (e^{x^{5} s i n (x)}))

What is the derivative of (3x^2/(5x^2+7x)) ?
The derivative of (3x^2/(5x^2+7x)) is (21)/((5x+7)^2)
What is the first derivative of (3x^2/(5x^2+7x)) ?
The first derivative of (3x^2/(5x^2+7x)) is (21)/((5x+7)^2)