What is the derivative of e^{2(x-1^2}+x/(1+x^3)) ?

The derivative of e^{2(x-1^2}+x/(1+x^3)) is e^{2(x-1)^2}*4(x-1)+(1-2x^3)/((1+x^3)^2)

What is the first derivative of e^{2(x-1^2}+x/(1+x^3)) ?

The first derivative of e^{2(x-1^2}+x/(1+x^3)) is e^{2(x-1)^2}*4(x-1)+(1-2x^3)/((1+x^3)^2)

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\frac{d}{d x} (e^{2 (x - 1)^{2}} + \frac{x}{1 + x ^{3}})

e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

Solution steps

\frac{d}{d x} (e^{2 (x - 1)^{2}} + \frac{x}{1 + x ^{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{2 (x - 1)^{2}}) + \frac{d}{d x} (\frac{x}{1 + x ^{3}})

\frac{d}{d x} (e^{2 (x - 1)^{2}}) = e^{2 (x - 1)^{2}} \cdot 4 (x - 1)

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

= e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

What is the derivative of e^{2(x-1^2}+x/(1+x^3)) ?
The derivative of e^{2(x-1^2}+x/(1+x^3)) is e^{2(x-1)^2}*4(x-1)+(1-2x^3)/((1+x^3)^2)
What is the first derivative of e^{2(x-1^2}+x/(1+x^3)) ?
The first derivative of e^{2(x-1^2}+x/(1+x^3)) is e^{2(x-1)^2}*4(x-1)+(1-2x^3)/((1+x^3)^2)