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

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

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

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

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derivative of

\frac{7 x ^{2} + 5 x + 3}{x}

\frac{21 x ^{2} + 5 x - 3}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (7 x^{2} + 5 x + 3) = 14 x + 5

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

= \frac{( 14 x + 5 ) x - \frac{1}{2 x} ( 7 x ^{2} + 5 x + 3 )}{( x ) ^{2}}

Simplify

\frac{( 14 x + 5 ) x - \frac{1}{2 x} ( 7 x ^{2} + 5 x + 3 )}{( x ) ^{2}} : \frac{21 x ^{2} + 5 x - 3}{2 x x}

= \frac{21 x ^{2} + 5 x - 3}{2 x x}

y^{^{''}} + 9 y = cos (10 t)

\frac{d}{d x} (\frac{sin ( x )}{x + tan ( x )})

\frac{\partial}{\partial x} (\frac{3}{t})

\int \frac{3}{x - 2} d x

y = e^{e^{4 x^{4}}}

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