What is the derivative of (x/3+6sqrt(x)^3) ?

The derivative of (x/3+6sqrt(x)^3) is (x^2)/9+5x^{3/2}+72x+324sqrt(x)

What is the first derivative of (x/3+6sqrt(x)^3) ?

The first derivative of (x/3+6sqrt(x)^3) is (x^2)/9+5x^{3/2}+72x+324sqrt(x)

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\frac{d}{d x} ((\frac{x}{3} + 6 x)^{3})

\frac{x ^{2}}{9} + 5 x^{\frac{3}{2}} + 72 x + 324 x

Solution steps

\frac{d}{d x} ((\frac{x}{3} + 6 x)^{3})

Simplify

(\frac{x}{3} + 6 x)^{3} : \frac{x ^{3}}{27} + 2 x^{\frac{5}{2}} + 36 x^{2} + 216 x^{\frac{3}{2}}

= \frac{d}{d x} (\frac{x ^{3}}{27} + 2 x^{\frac{5}{2}} + 36 x^{2} + 216 x^{\frac{3}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{27}) + \frac{d}{d x} (2 x^{\frac{5}{2}}) + \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (216 x^{\frac{3}{2}})

\frac{d}{d x} (\frac{x ^{3}}{27}) = \frac{x ^{2}}{9}

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

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (216 x^{\frac{3}{2}}) = 324 x

= \frac{x ^{2}}{9} + 5 x^{\frac{3}{2}} + 72 x + 324 x

\int_{0}^{\frac{π}{8}} (sin (2 x)) d x

\frac{d}{d x} (\frac{x}{x ^{- 1} + 5})

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

\int_{- 1}^{1} (9 x^{2} + 6 x - 3) d x

t e^{4 t}

What is the derivative of (x/3+6sqrt(x)^3) ?
The derivative of (x/3+6sqrt(x)^3) is (x^2)/9+5x^{3/2}+72x+324sqrt(x)
What is the first derivative of (x/3+6sqrt(x)^3) ?
The first derivative of (x/3+6sqrt(x)^3) is (x^2)/9+5x^{3/2}+72x+324sqrt(x)