What is (\partial)/(\partial x)(2xe^{ay}a+3e^{xb}) ?

The answer to (\partial)/(\partial x)(2xe^{ay}a+3e^{xb}) is 2ae^{ay}+3e^{xb}b

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(\partial)/(\partial x)(2xe^{ay}a+3e^{xb})

\frac{\partial}{\partial x} (2 x e^{a y} a + 3 e^{x b})

2 a e^{a y} + 3 e^{x b} b

Solution steps

\frac{\partial}{\partial x} (2 x e^{a y} a + 3 e^{x b})

Treat

a, y, b

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x e^{a y} a) + \frac{\partial}{\partial x} (3 e^{x b})

\frac{\partial}{\partial x} (2 x e^{a y} a) = 2 a e^{a y}

\frac{\partial}{\partial x} (3 e^{x b}) = 3 e^{x b} b

= 2 a e^{a y} + 3 e^{x b} b

\frac{2 d y}{d x} = y^{2}

\frac{d}{d x} (3 - ln (6 x) - \frac{x ^{2}}{12} + x)

\int \frac{1 + ln ( x )}{x} d x

3 t^{2} + 25

What is (\partial)/(\partial x)(2xe^{ay}a+3e^{xb}) ?
The answer to (\partial)/(\partial x)(2xe^{ay}a+3e^{xb}) is 2ae^{ay}+3e^{xb}b