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Popular >

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

Solution

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

Solution

e^{x^{3 + 6 x^{2}}} x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{3 + 6 x^{2}}) = x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

= e^{x^{3 + 6 x^{2}}} x^{3 + 6 x^{2}} (12 x ln (x) + \frac{3 + 6 x ^{2}}{x})

Popular Examples

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(\partial)/(\partial x)((13x-1)(3y-1))

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\int \frac{2 x ^{3} - x ^{2} + 2 x + 2}{x ^{2} + 1} d x

taylor 1/(x-1),10 taylor

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Frequently Asked Questions (FAQ)

What is the derivative of e^{x^{3+6x^2}} ?
The derivative of e^{x^{3+6x^2}} is e^{x^{3+6x^2}}x^{3+6x^2}(12xln(x)+(3+6x^2)/x)
What is the first derivative of e^{x^{3+6x^2}} ?
The first derivative of e^{x^{3+6x^2}} is e^{x^{3+6x^2}}x^{3+6x^2}(12xln(x)+(3+6x^2)/x)