What is the derivative of f(x)=xe^{3x^2}+1 ?

The derivative of f(x)=xe^{3x^2}+1 is 6e^{3x^2}x^2+e^{3x^2}

What is the first derivative of f(x)=xe^{3x^2}+1 ?

The first derivative of f(x)=xe^{3x^2}+1 is 6e^{3x^2}x^2+e^{3x^2}

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derivative of

f (x) = x e^{3 x^{2}} + 1

6 e^{3 x^{2}} x^{2} + e^{3 x^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

= e^{3 x^{2}} + 6 e^{3 x^{2}} x^{2} + 0

Simplify

= 6 e^{3 x^{2}} x^{2} + e^{3 x^{2}}

\frac{4}{x ^{5}} - \frac{1}{x ^{2}}

\int \frac{cos ( x )}{1 + 8 sin ( x )} d x

\frac{d y}{d x} = (\frac{x}{y})

\frac{4}{x}, 1

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

What is the derivative of f(x)=xe^{3x^2}+1 ?
The derivative of f(x)=xe^{3x^2}+1 is 6e^{3x^2}x^2+e^{3x^2}
What is the first derivative of f(x)=xe^{3x^2}+1 ?
The first derivative of f(x)=xe^{3x^2}+1 is 6e^{3x^2}x^2+e^{3x^2}