What is the derivative of 3xarctan(x^2+e^{sin(x)}) ?

The derivative of 3xarctan(x^2+e^{sin(x)}) is 3(arctan(x^2)+(2x^2)/(x^4+1))+e^{sin(x)}cos(x)

What is the first derivative of 3xarctan(x^2+e^{sin(x)}) ?

The first derivative of 3xarctan(x^2+e^{sin(x)}) is 3(arctan(x^2)+(2x^2)/(x^4+1))+e^{sin(x)}cos(x)

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\frac{d}{d x} (3 x arctan (x^{2}) + e^{s i n (x)})

3 (arctan (x^{2}) + \frac{2 x ^{2}}{x ^{4} + 1}) + e^{s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (3 x arctan (x^{2}) + e^{s i n (x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x arctan (x^{2})) + \frac{d}{d x} (e^{s i n (x)})

\frac{d}{d x} (3 x arctan (x^{2})) = 3 (arctan (x^{2}) + \frac{2 x ^{2}}{x ^{4} + 1})

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

= 3 (arctan (x^{2}) + \frac{2 x ^{2}}{x ^{4} + 1}) + e^{s i n (x)} cos (x)

\int 3 x x + 5 d x

\frac{d}{d x} (x ln (x^{3}))

\int_{1}^{\infty} x e^{- 14 x} d x

13 (t + 1) \frac{d y}{d t} - 9 y = 36 t

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What is the derivative of 3xarctan(x^2+e^{sin(x)}) ?
The derivative of 3xarctan(x^2+e^{sin(x)}) is 3(arctan(x^2)+(2x^2)/(x^4+1))+e^{sin(x)}cos(x)
What is the first derivative of 3xarctan(x^2+e^{sin(x)}) ?
The first derivative of 3xarctan(x^2+e^{sin(x)}) is 3(arctan(x^2)+(2x^2)/(x^4+1))+e^{sin(x)}cos(x)