What is the derivative of x^8arctan(x^3) ?

The derivative of x^8arctan(x^3) is 8x^7arctan(x^3)+(3x^{10})/(x^6+1)

What is the first derivative of x^8arctan(x^3) ?

The first derivative of x^8arctan(x^3) is 8x^7arctan(x^3)+(3x^{10})/(x^6+1)

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\frac{d}{d x} (x^{8} arctan (x^{3}))

8 x^{7} arctan (x^{3}) + \frac{3 x ^{10}}{x ^{6} + 1}

Solution steps

\frac{d}{d x} (x^{8} arctan (x^{3}))

Apply the Product Rule:

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

f = x^{8}, g = arctan (x^{3})

= \frac{d}{d x} (x^{8}) arctan (x^{3}) + \frac{d}{d x} (arctan (x^{3})) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (arctan (x^{3})) = \frac{3 x ^{2}}{x ^{6} + 1}

= 8 x^{7} arctan (x^{3}) + \frac{3 x ^{2}}{x ^{6} + 1} x^{8}

\frac{3 x ^{2}}{x ^{6} + 1} x^{8} = \frac{3 x ^{10}}{x ^{6} + 1}

= 8 x^{7} arctan (x^{3}) + \frac{3 x ^{10}}{x ^{6} + 1}

y^{^{'}} = k (y - 70)

\int \frac{ln ( 8 x )}{x} d x

\frac{\partial}{\partial z} (e^{yz})

y = ln (\frac{x - 1}{x + 3}) - x

x \to c lim (\frac{13}{3} + \frac{2}{3})

What is the derivative of x^8arctan(x^3) ?
The derivative of x^8arctan(x^3) is 8x^7arctan(x^3)+(3x^{10})/(x^6+1)
What is the first derivative of x^8arctan(x^3) ?
The first derivative of x^8arctan(x^3) is 8x^7arctan(x^3)+(3x^{10})/(x^6+1)