What is the derivative of e^{x^2}sin(x^3-2) ?

The derivative of e^{x^2}sin(x^3-2) is e^{x^2}*2xsin(x^3-2)+cos(x^3-2)*3x^2e^{x^2}

What is the first derivative of e^{x^2}sin(x^3-2) ?

The first derivative of e^{x^2}sin(x^3-2) is e^{x^2}*2xsin(x^3-2)+cos(x^3-2)*3x^2e^{x^2}

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\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

e^{x^{2}} \cdot 2 x sin (x^{3} - 2) + cos (x^{3} - 2) \cdot 3 x^{2} e^{x^{2}}

Solution steps

\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

Apply the Product Rule:

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

f = e^{x^{2}}, g = sin (x^{3} - 2)

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

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

\frac{d}{d x} (sin (x^{3} - 2)) = cos (x^{3} - 2) \cdot 3 x^{2}

= e^{x^{2}} \cdot 2 x sin (x^{3} - 2) + cos (x^{3} - 2) \cdot 3 x^{2} e^{x^{2}}

What is the derivative of e^{x^2}sin(x^3-2) ?
The derivative of e^{x^2}sin(x^3-2) is e^{x^2}*2xsin(x^3-2)+cos(x^3-2)*3x^2e^{x^2}
What is the first derivative of e^{x^2}sin(x^3-2) ?
The first derivative of e^{x^2}sin(x^3-2) is e^{x^2}*2xsin(x^3-2)+cos(x^3-2)*3x^2e^{x^2}