What is the derivative of e^{x^2sin(x}) ?

The derivative of e^{x^2sin(x}) is e^{x^2sin(x)}(2xsin(x)+cos(x)x^2)

What is the first derivative of e^{x^2sin(x}) ?

The first derivative of e^{x^2sin(x}) is e^{x^2sin(x)}(2xsin(x)+cos(x)x^2)

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\frac{d}{d x} (e^{x^{2} s i n (x)})

e^{x^{2} s i n (x)} (2 x sin (x) + cos (x) x^{2})

Solution steps

\frac{d}{d x} (e^{x^{2} s i n (x)})

Apply the chain rule:

e^{x^{2} s i n (x)} \frac{d}{d x} (x^{2} sin (x))

= e^{x^{2} s i n (x)} \frac{d}{d x} (x^{2} sin (x))

\frac{d}{d x} (x^{2} sin (x)) = 2 x sin (x) + cos (x) x^{2}

= e^{x^{2} s i n (x)} (2 x sin (x) + cos (x) x^{2})

What is the derivative of e^{x^2sin(x}) ?
The derivative of e^{x^2sin(x}) is e^{x^2sin(x)}(2xsin(x)+cos(x)x^2)
What is the first derivative of e^{x^2sin(x}) ?
The first derivative of e^{x^2sin(x}) is e^{x^2sin(x)}(2xsin(x)+cos(x)x^2)