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

The answer to (\partial)/(\partial x)(5x^3y+3sin(xy)) is 15yx^2+3cos(xy)y

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

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

15 y x^{2} + 3 cos (x y) y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{3} y) = 15 y x^{2}

\frac{\partial}{\partial x} (3 sin (x y)) = 3 cos (x y) y

= 15 y x^{2} + 3 cos (x y) y

\int (2^{x} - 2)^{2} d x

\int x \cdot cos (x^{2} + 1) d x

\int \frac{3 x - 1}{4 x ^{2} - 4 x + 17} d x

\frac{d y}{d x} = \frac{( 3 - y )}{2 x}

100 y^{^{''}} + 20 y^{^{'}} + y = 0

What is (\partial)/(\partial x)(5x^3y+3sin(xy)) ?
The answer to (\partial)/(\partial x)(5x^3y+3sin(xy)) is 15yx^2+3cos(xy)y