What is (\partial)/(\partial x)(4x^2e^{ay}+3e^{bx}) ?

The answer to (\partial)/(\partial x)(4x^2e^{ay}+3e^{bx}) is 8e^{ay}x+3e^{bx}b

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(\partial)/(\partial x)(4x^2e^{ay}+3e^{bx})

\frac{\partial}{\partial x} (4 x^{2} e^{a y} + 3 e^{b x})

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

Solution steps

\frac{\partial}{\partial x} (4 x^{2} e^{a y} + 3 e^{b x})

Treat

a, y, b

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{2} e^{a y}) + \frac{\partial}{\partial x} (3 e^{b x})

\frac{\partial}{\partial x} (4 x^{2} e^{a y}) = 8 e^{a y} x

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

= 8 e^{a y} x + 3 e^{b x} b

What is (\partial)/(\partial x)(4x^2e^{ay}+3e^{bx}) ?
The answer to (\partial)/(\partial x)(4x^2e^{ay}+3e^{bx}) is 8e^{ay}x+3e^{bx}b