What is (\partial)/(\partial x)(8xe^{5xy}) ?

The answer to (\partial)/(\partial x)(8xe^{5xy}) is 8(e^{5xy}+5e^{5xy}xy)

Popular >

(\partial)/(\partial x)(8xe^{5xy})

\frac{\partial}{\partial x} (8 x e^{5 x y})

8 (e^{5 x y} + 5 e^{5 x y} x y)

Solution steps

\frac{\partial}{\partial x} (8 x e^{5 x y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{\partial}{\partial x} (x e^{5 x y})

Apply the Product Rule:

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

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

= 8 (\frac{\partial}{\partial x} (x) e^{5 x y} + \frac{\partial}{\partial x} (e^{5 x y}) x)

\frac{\partial}{\partial x} (x) = 1

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

= 8 (1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x)

Simplify

= 8 (e^{5 x y} + 5 e^{5 x y} x y)

n = 0 \sum \infty \frac{n !}{1 1 ^{n}}

y = 2 e^{2 e^{x} + x}

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

f (x) = 3 x^{4} + 2 x - 1, (2, 51)

\int (tan (x))^{7} (sec (x))^{2} d x

What is (\partial)/(\partial x)(8xe^{5xy}) ?
The answer to (\partial)/(\partial x)(8xe^{5xy}) is 8(e^{5xy}+5e^{5xy}xy)