What is the derivative of x^2arctan(5x+ln(1+4x^2)) ?

The derivative of x^2arctan(5x+ln(1+4x^2)) is 2xarctan(5x)+(5x^2)/(25x^2+1)+(8x)/(1+4x^2)

What is the first derivative of x^2arctan(5x+ln(1+4x^2)) ?

The first derivative of x^2arctan(5x+ln(1+4x^2)) is 2xarctan(5x)+(5x^2)/(25x^2+1)+(8x)/(1+4x^2)

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\frac{d}{d x} (x^{2} arctan (5 x) + ln (1 + 4 x^{2}))

2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1} + \frac{8 x}{1 + 4 x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} arctan (5 x) + ln (1 + 4 x^{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2} arctan (5 x)) + \frac{d}{d x} (ln (1 + 4 x^{2}))

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

\frac{d}{d x} (ln (1 + 4 x^{2})) = \frac{8 x}{1 + 4 x ^{2}}

= 2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1} + \frac{8 x}{1 + 4 x ^{2}}

\frac{d}{d x} (9 sin (4 x))

\frac{36}{( 1 + 3 x ) ^{3}}

\int \frac{26}{( x ^{2} - 1 ) ^{2}} d x

\frac{0.07 s}{7 s ^{2} + 19980}

e^{- 7 x}, x \geq 0

What is the derivative of x^2arctan(5x+ln(1+4x^2)) ?
The derivative of x^2arctan(5x+ln(1+4x^2)) is 2xarctan(5x)+(5x^2)/(25x^2+1)+(8x)/(1+4x^2)
What is the first derivative of x^2arctan(5x+ln(1+4x^2)) ?
The first derivative of x^2arctan(5x+ln(1+4x^2)) is 2xarctan(5x)+(5x^2)/(25x^2+1)+(8x)/(1+4x^2)