What is (\partial)/(\partial x)(Ax+By+Ce^{xy}) ?

The answer to (\partial)/(\partial x)(Ax+By+Ce^{xy}) is Ce^{xy}y+A

Popular >

(\partial)/(\partial x)(Ax+By+Ce^{xy})

\frac{\partial}{\partial x} (A x + B y + C e^{x y})

C e^{x y} y + A

Solution steps

\frac{\partial}{\partial x} (A x + B y + C e^{x y})

Treat

A, B, C, y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (A x) + \frac{\partial}{\partial x} (B y) + \frac{\partial}{\partial x} (C e^{x y})

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

\frac{\partial}{\partial x} (B y) = 0

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

= A + 0 + C e^{x y} y

Simplify

= C e^{x y} y + A

\int_{0}^{5} \frac{1}{x ^{\frac{5}{2}}} d x

\int 3 x^{2} - 4 x + 1 d x

f (x) = (x^{2} + x + 1)^{3}

sin (ω \cdot t)

\int \frac{x ^{2} + x}{x - 1} d x

What is (\partial)/(\partial x)(Ax+By+Ce^{xy}) ?
The answer to (\partial)/(\partial x)(Ax+By+Ce^{xy}) is Ce^{xy}y+A