What is the derivative of e^{x^3}y ?

The derivative of e^{x^3}y is e^{x^3}*3x^2y+(dy)/(dx)e^{x^3}

What is the first derivative of e^{x^3}y ?

The first derivative of e^{x^3}y is e^{x^3}*3x^2y+(dy)/(dx)e^{x^3}

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\frac{d}{d x} (e^{x^{3}} y)

e^{x^{3}} \cdot 3 x^{2} y + \frac{d y}{d x} e^{x^{3}}

Solution steps

\frac{d}{d x} (e^{x^{3}} y)

Apply the Product Rule:

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

f = e^{x^{3}}, g = y

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

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

= e^{x^{3}} \cdot 3 x^{2} y + \frac{d y}{d x} e^{x^{3}}

\int 10 x^{\frac{3}{2}} + 6 x - 8 d x

\int \frac{5}{x} + sec^{2} (x) d x

x \to 1 lim (\frac{- 3 x}{x - 1})

v^{'} = v^{2}

x \to 2 lim (2 x^{2})

What is the derivative of e^{x^3}y ?
The derivative of e^{x^3}y is e^{x^3}*3x^2y+(dy)/(dx)e^{x^3}
What is the first derivative of e^{x^3}y ?
The first derivative of e^{x^3}y is e^{x^3}*3x^2y+(dy)/(dx)e^{x^3}