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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

f = e^{2 x}, g = x^{3} + 1

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

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

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

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

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