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

The derivative of (3x^2+5x+7/(sqrt(x))) is (9x^2+5x-7)/(2xsqrt(x))

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

The first derivative of (3x^2+5x+7/(sqrt(x))) is (9x^2+5x-7)/(2xsqrt(x))

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

\frac{9 x ^{2} + 5 x - 7}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x^{2} + 5 x + 7) = 6 x + 5

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

= \frac{( 6 x + 5 ) x - \frac{1}{2 x} ( 3 x ^{2} + 5 x + 7 )}{( x ) ^{2}}

Simplify

\frac{( 6 x + 5 ) x - \frac{1}{2 x} ( 3 x ^{2} + 5 x + 7 )}{( x ) ^{2}} : \frac{9 x ^{2} + 5 x - 7}{2 x x}

= \frac{9 x ^{2} + 5 x - 7}{2 x x}

\int_{0}^{\frac{π}{12}} \frac{sin ( 6 x )}{1 + cos ^{2} ( 6 x )} d x

3 y^{^{''}} - 2 y^{^{'}} + 4 y = 0

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

\int \frac{1}{- x ^{2} + 4 x + 12} d x

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

What is the derivative of (3x^2+5x+7/(sqrt(x))) ?
The derivative of (3x^2+5x+7/(sqrt(x))) is (9x^2+5x-7)/(2xsqrt(x))
What is the first derivative of (3x^2+5x+7/(sqrt(x))) ?
The first derivative of (3x^2+5x+7/(sqrt(x))) is (9x^2+5x-7)/(2xsqrt(x))