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Popular >

derivative of e^{xy}y

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

Popular Examples

integral of (x+3)sqrt(7-x)

\int (x + 3) 7 - x d x

limit as x approaches 0 of x^4sin(3/x)

x \to 0 lim (x^{4} sin (\frac{3}{x}))

derivative of (2x^3+5^4)

\frac{d}{d x} ((2 x^{3} + 5)^{4})

integral of (sin(x))/(cos^2(x)-3cos(x))

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

tangent of f(x)=sqrt(x^2-x+4),\at x=4 tangent of

f (x) = x^{2} - x + 4, at x = 4

Frequently Asked Questions (FAQ)

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