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

The derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) is (3x^9-49+30x^{17/2}sqrt(x))/(2x^{9/2)}

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

The first derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) is (3x^9-49+30x^{17/2}sqrt(x))/(2x^{9/2)}

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derivative of

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

\frac{3 x ^{9} - 49 + 30 x ^{\frac{17}{2}} x}{2 x ^{\frac{9}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (3 x^{5} x) = 3 (5 x^{4} x + \frac{x ^{\frac{9}{2}}}{2})

\frac{d}{d x} (\frac{7}{x ^{3} x}) = - \frac{49}{2 x ^{\frac{9}{2}}}

= 3 (5 x^{4} x + \frac{x ^{\frac{9}{2}}}{2}) - \frac{49}{2 x ^{\frac{9}{2}}}

Simplify

3 (5 x^{4} x + \frac{x ^{\frac{9}{2}}}{2}) - \frac{49}{2 x ^{\frac{9}{2}}} : \frac{3 x ^{9} - 49 + 30 x ^{\frac{17}{2}} x}{2 x ^{\frac{9}{2}}}

= \frac{3 x ^{9} - 49 + 30 x ^{\frac{17}{2}} x}{2 x ^{\frac{9}{2}}}

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

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

\frac{6}{s ^{2} + 5 s + 4}

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

\int_{- 4}^{0} \frac{1}{( x + 2 ) ^{\frac{1}{3}}} d x

What is the derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) ?
The derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) is (3x^9-49+30x^{17/2}sqrt(x))/(2x^{9/2)}
What is the first derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) ?
The first derivative of 3x^5sqrt(x)+7/(x^3sqrt(x)) is (3x^9-49+30x^{17/2}sqrt(x))/(2x^{9/2)}