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Popular >

derivative of xe^{3y}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{3 y} + e^{3 y} \cdot 3 \frac{d y}{d x} x

Simplify

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

Popular Examples

(dy)/(dx)=y^2(4x+1)

\frac{d y}{d x} = y^{2} (4 x + 1)

1/t y^'= y/(t^2)-1/y

\frac{1}{t} y^{^{'}} = \frac{y}{t ^{2}} - \frac{1}{y}

tangent of f(x)= 1/(5+3x),(1, 1/8)tangent of

f (x) = \frac{1}{5 + 3 x}, (1, \frac{1}{8})

inverse oflaplace-2/(s+1/3)inverse laplace

- \frac{2}{s + \frac{1}{3}}

(\partial)/(\partial x)(sin(pi(2x-3y)))

\frac{\partial}{\partial x} (sin (π (2 x - 3 y)))

Frequently Asked Questions (FAQ)

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