What is the derivative of (21x^2+6x-6)/(2xsqrt(x)) ?

The derivative of (21x^2+6x-6)/(2xsqrt(x)) is (3(7x^2-2x+6))/(4x^{5/2)}

What is the first derivative of (21x^2+6x-6)/(2xsqrt(x)) ?

The first derivative of (21x^2+6x-6)/(2xsqrt(x)) is (3(7x^2-2x+6))/(4x^{5/2)}

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derivative of

\frac{21 x ^{2} + 6 x - 6}{2 x x}

\frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{21 x ^{2} + 6 x - 6}{2 x x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{21 x ^{2} + 6 x - 6}{x x})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 21 x ^{2} + 6 x - 6 ) x x - \frac{d}{d x} ( x x ) ( 21 x ^{2} + 6 x - 6 )}{( x x ) ^{2}}

\frac{d}{d x} (21 x^{2} + 6 x - 6) = 42 x + 6

\frac{d}{d x} (x x) = \frac{3 x}{2}

= \frac{1}{2} \cdot \frac{( 42 x + 6 ) x x - \frac{3 x}{2} ( 21 x ^{2} + 6 x - 6 )}{( x x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( 42 x + 6 ) x x - \frac{3 x}{2} ( 21 x ^{2} + 6 x - 6 )}{( x x ) ^{2}} : \frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

= \frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

\int \frac{1}{9 x ^{2} - 25} d x

\int \frac{1}{x + 1 + x - 1} d x

f (x) = x^{2} - 1, g (x) = - x + 2, 0, 1

\int (2 - x) 3^{(2 - x)^{2}} d x

\int_{0}^{3} \frac{1}{9 - x ^{2}} d x

What is the derivative of (21x^2+6x-6)/(2xsqrt(x)) ?
The derivative of (21x^2+6x-6)/(2xsqrt(x)) is (3(7x^2-2x+6))/(4x^{5/2)}
What is the first derivative of (21x^2+6x-6)/(2xsqrt(x)) ?
The first derivative of (21x^2+6x-6)/(2xsqrt(x)) is (3(7x^2-2x+6))/(4x^{5/2)}