What is the derivative of e^xsin(x^2) ?

The derivative of e^xsin(x^2) is e^xsin(x^2)+cos(x^2)*2xe^x

What is the first derivative of e^xsin(x^2) ?

The first derivative of e^xsin(x^2) is e^xsin(x^2)+cos(x^2)*2xe^x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{d}{d x} (2 x + sin (2 x))

\frac{\partial}{\partial y} (x e^{7 x y})

\int e^{(x - 1)} d x

\frac{d y}{d x} = y e^{- x^{2}}

\frac{\partial}{\partial x} (e^{x + y + 9})

What is the derivative of e^xsin(x^2) ?
The derivative of e^xsin(x^2) is e^xsin(x^2)+cos(x^2)*2xe^x
What is the first derivative of e^xsin(x^2) ?
The first derivative of e^xsin(x^2) is e^xsin(x^2)+cos(x^2)*2xe^x