What is the derivative of (xe^{2x}+x^3^6) ?

The derivative of (xe^{2x}+x^3^6) is 6(xe^{2x}+x^3)^5(e^{2x}+2e^{2x}x+3x^2)

What is the first derivative of (xe^{2x}+x^3^6) ?

The first derivative of (xe^{2x}+x^3^6) is 6(xe^{2x}+x^3)^5(e^{2x}+2e^{2x}x+3x^2)

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

6 (x e^{2 x} + x^{3})^{5} (e^{2 x} + 2 e^{2 x} x + 3 x^{2})

Solution steps

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

Apply the chain rule:

6 (x e^{2 x} + x^{3})^{5} \frac{d}{d x} (x e^{2 x} + x^{3})

= 6 (x e^{2 x} + x^{3})^{5} \frac{d}{d x} (x e^{2 x} + x^{3})

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

= 6 (x e^{2 x} + x^{3})^{5} (e^{2 x} + 2 e^{2 x} x + 3 x^{2})

What is the derivative of (xe^{2x}+x^3^6) ?
The derivative of (xe^{2x}+x^3^6) is 6(xe^{2x}+x^3)^5(e^{2x}+2e^{2x}x+3x^2)
What is the first derivative of (xe^{2x}+x^3^6) ?
The first derivative of (xe^{2x}+x^3^6) is 6(xe^{2x}+x^3)^5(e^{2x}+2e^{2x}x+3x^2)