What is the derivative of sqrt(x)(x^4+1/(x^2)) ?

The derivative of sqrt(x)(x^4+1/(x^2)) is (x^6+8x^{11/2}sqrt(x)-3)/(2x^{5/2)}

What is the first derivative of sqrt(x)(x^4+1/(x^2)) ?

The first derivative of sqrt(x)(x^4+1/(x^2)) is (x^6+8x^{11/2}sqrt(x)-3)/(2x^{5/2)}

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\frac{d}{d x} (x (x^{4} + \frac{1}{x ^{2}}))

\frac{x ^{6} + 8 x ^{\frac{11}{2}} x - 3}{2 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (x (x^{4} + \frac{1}{x ^{2}}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{4} + \frac{1}{x ^{2}}

= \frac{d}{d x} (x) (x^{4} + \frac{1}{x ^{2}}) + \frac{d}{d x} (x^{4} + \frac{1}{x ^{2}}) x

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

\frac{d}{d x} (x^{4} + \frac{1}{x ^{2}}) = 4 x^{3} - \frac{2}{x ^{3}}

= \frac{1}{2 x} (x^{4} + \frac{1}{x ^{2}}) + (4 x^{3} - \frac{2}{x ^{3}}) x

Simplify

\frac{1}{2 x} (x^{4} + \frac{1}{x ^{2}}) + (4 x^{3} - \frac{2}{x ^{3}}) x : \frac{x ^{6} + 8 x ^{\frac{11}{2}} x - 3}{2 x ^{\frac{5}{2}}}

= \frac{x ^{6} + 8 x ^{\frac{11}{2}} x - 3}{2 x ^{\frac{5}{2}}}

\int (x^{5} ln (x)) d x

\int_{0}^{1} \frac{2}{x ( 1 + x )} d x

f (x) = arcsin (x)

\frac{2}{4 s ^{2} - 8 s}

\int_{2}^{4} \frac{( 2 x - 3 ) x}{6} d x

What is the derivative of sqrt(x)(x^4+1/(x^2)) ?
The derivative of sqrt(x)(x^4+1/(x^2)) is (x^6+8x^{11/2}sqrt(x)-3)/(2x^{5/2)}
What is the first derivative of sqrt(x)(x^4+1/(x^2)) ?
The first derivative of sqrt(x)(x^4+1/(x^2)) is (x^6+8x^{11/2}sqrt(x)-3)/(2x^{5/2)}