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Popular >

derivative of xe^{5y}

Solution

\frac{d}{d x} (x e^{5 y})

Solution

e^{5 y} + 5 e^{5 y} x \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x e^{5 y})

Apply the Product Rule:

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

f = x, g = e^{5 y}

= \frac{d x}{d x} e^{5 y} + \frac{d}{d x} (e^{5 y}) x

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

\frac{d}{d x} (e^{5 y}) = e^{5 y} \cdot 5 \frac{d y}{d x}

= 1 \cdot e^{5 y} + e^{5 y} \cdot 5 \frac{d y}{d x} x

Simplify

= e^{5 y} + 5 e^{5 y} x \frac{d y}{d x}

Popular Examples

tangent of y=(4x)/(x+3),(1,1)tangent of

y = \frac{4 x}{x + 3}, (1, 1)

integral of x^2e^{x^{3+4}}

\int x^{2} e^{x^{3 + 4}} d x

tangent of f(x)=log_{2}(2x^2+14),\at x=5 tangent of

f (x) = lo g_{2} (2 x^{2} + 14), at x = 5

limit as x approaches 2 of 0/4

x \to 2 lim (\frac{0}{4})

taylor 1/(x-1),5 taylor

\frac{1}{x - 1}, 5

Frequently Asked Questions (FAQ)

What is the derivative of xe^{5y} ?
The derivative of xe^{5y} is e^{5y}+5e^{5y}x(dy)/(dx)
What is the first derivative of xe^{5y} ?
The first derivative of xe^{5y} is e^{5y}+5e^{5y}x(dy)/(dx)