What is the derivative of 2x^4arctan(5x^3) ?

The derivative of 2x^4arctan(5x^3) is 2(4x^3arctan(5x^3)+(15x^6)/(25x^6+1))

What is the first derivative of 2x^4arctan(5x^3) ?

The first derivative of 2x^4arctan(5x^3) is 2(4x^3arctan(5x^3)+(15x^6)/(25x^6+1))

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derivative of

2 x^{4} arctan (5 x^{3})

2 (4 x^{3} arctan (5 x^{3}) + \frac{15 x ^{6}}{25 x ^{6} + 1})

Solution steps

\frac{d}{d x} (2 x^{4} arctan (5 x^{3}))

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{4}, g = arctan (5 x^{3})

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (arctan (5 x^{3})) = \frac{15 x ^{2}}{25 x ^{6} + 1}

= 2 (4 x^{3} arctan (5 x^{3}) + \frac{15 x ^{2}}{25 x ^{6} + 1} x^{4})

\frac{15 x ^{2}}{25 x ^{6} + 1} x^{4} = \frac{15 x ^{6}}{25 x ^{6} + 1}

= 2 (4 x^{3} arctan (5 x^{3}) + \frac{15 x ^{6}}{25 x ^{6} + 1})

\int ln^{2} (2 x) d x

\frac{d}{d u} (uv)

x \to 0 lim (- \frac{sin ( x )}{3 x})

\int x x + 9 d x

x \to - 1 lim (x^{2} - 5 x + 6)

What is the derivative of 2x^4arctan(5x^3) ?
The derivative of 2x^4arctan(5x^3) is 2(4x^3arctan(5x^3)+(15x^6)/(25x^6+1))
What is the first derivative of 2x^4arctan(5x^3) ?
The first derivative of 2x^4arctan(5x^3) is 2(4x^3arctan(5x^3)+(15x^6)/(25x^6+1))