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

The derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) is (12x^2+7x-7)/(2xsqrt(x))

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

The first derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) is (12x^2+7x-7)/(2xsqrt(x))

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derivative of

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

\frac{12 x ^{2} + 7 x - 7}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{( 8 x + 7 ) x - \frac{1}{2 x} ( 4 x ^{2} + 7 x + 7 )}{( x ) ^{2}}

Simplify

\frac{( 8 x + 7 ) x - \frac{1}{2 x} ( 4 x ^{2} + 7 x + 7 )}{( x ) ^{2}} : \frac{12 x ^{2} + 7 x - 7}{2 x x}

= \frac{12 x ^{2} + 7 x - 7}{2 x x}

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

\int sin^{3} (2 θ) cos (2 θ) d θ

\int (4 sin (x)) d x

\frac{\partial}{\partial x} (2 sin^{2} (x))

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

What is the derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) ?
The derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) is (12x^2+7x-7)/(2xsqrt(x))
What is the first derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) ?
The first derivative of f(5)=(4x^2+7x+7)/(sqrt(x)) is (12x^2+7x-7)/(2xsqrt(x))