What is (\partial)/(\partial x)(5x^2+y+sin(axy)+3) ?

The answer to (\partial)/(\partial x)(5x^2+y+sin(axy)+3) is aycos(axy)+10x

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(\partial)/(\partial x)(5x^2+y+sin(axy)+3)

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

a y cos (a x y) + 10 x

Solution steps

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

Treat

a, y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (sin (a x y)) + \frac{\partial}{\partial x} (3)

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

\frac{\partial}{\partial x} (sin (a x y)) = cos (a x y) a y

\frac{\partial}{\partial x} (3) = 0

= 10 x + 0 + cos (a x y) a y + 0

Simplify

= a y cos (a x y) + 10 x

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\int \frac{x}{y} + \frac{y}{x} d y

\int_{0}^{2} x^{3} 1 + 9 x^{4} d x

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What is (\partial)/(\partial x)(5x^2+y+sin(axy)+3) ?
The answer to (\partial)/(\partial x)(5x^2+y+sin(axy)+3) is aycos(axy)+10x