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Popular >

derivative of xe^{xy+1}

Solution

\frac{d}{d x} (x e^{x y + 1})

Solution

e^{x y + 1} + e^{x y + 1} x (x \frac{d y}{d x} + y)

Solution steps

\frac{d}{d x} (x e^{x y + 1})

Apply the Product Rule:

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

f = x, g = e^{x y + 1}

= \frac{d x}{d x} e^{x y + 1} + \frac{d}{d x} (e^{x y + 1}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x y + 1}) = e^{x y + 1} (x \frac{d y}{d x} + y)

= 1 \cdot e^{x y + 1} + e^{x y + 1} (x \frac{d y}{d x} + y) x

Simplify

= e^{x y + 1} + e^{x y + 1} x (x \frac{d y}{d x} + y)

Popular Examples

tangent of f(x)=x^2-3x+2,\at x=2 tangent of

f (x) = x^{2} - 3 x + 2, at x = 2

integral of (2x-3)/6

\int \frac{2 x - 3}{6} d x

derivative of ln(x^2)derivative of

ln (x^{2})

inverse oflaplace 1/((s+3))inverse laplace

\frac{1}{( s + 3 )}

integral of 1/((2x-3)*(3x^2+x))

\int \frac{1}{( 2 x - 3 ) \cdot ( 3 x ^{2} + x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of xe^{xy+1} ?
The derivative of xe^{xy+1} is e^{xy+1}+e^{xy+1}x(x(dy)/(dx)+y)
What is the first derivative of xe^{xy+1} ?
The first derivative of xe^{xy+1} is e^{xy+1}+e^{xy+1}x(x(dy)/(dx)+y)