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Popular >

derivative of xe^{9xy}

Solution

\frac{d}{d x} (x e^{9 x y})

Solution

e^{9 x y} + 9 e^{9 x y} x (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (x e^{9 x y})

Apply the Product Rule:

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

f = x, g = e^{9 x y}

= \frac{d x}{d x} e^{9 x y} + \frac{d}{d x} (e^{9 x y}) x

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

\frac{d}{d x} (e^{9 x y}) = e^{9 x y} \cdot 9 (y + x \frac{d y}{d x})

= 1 \cdot e^{9 x y} + e^{9 x y} \cdot 9 (y + x \frac{d y}{d x}) x

Simplify

= e^{9 x y} + 9 e^{9 x y} x (y + x \frac{d y}{d x})

Popular Examples

integral of (2x-3)/(x^2+6x+13)

\int \frac{2 x - 3}{x ^{2} + 6 x + 13} d x

derivative of (x^2)/3 derivative of

\frac{x ^{2}}{3}

slope of (-12,5),(-4,-1)slope

(- 12, 5), (- 4, - 1)

area f(x)=x^2-12,g(x)=x-6 area

f (x) = x^{2} - 12, g (x) = x - 6

(\partial)/(\partial x)(sin(4x^3y-6xy^2))

\frac{\partial}{\partial x} (sin (4 x^{3} y - 6 x y^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of xe^{9xy} ?
The derivative of xe^{9xy} is e^{9xy}+9e^{9xy}x(y+x(dy)/(dx))
What is the first derivative of xe^{9xy} ?
The first derivative of xe^{9xy} is e^{9xy}+9e^{9xy}x(y+x(dy)/(dx))