What is (\partial)/(\partial x)(25x^8y^4+12x^4y^5) ?

The answer to (\partial)/(\partial x)(25x^8y^4+12x^4y^5) is 200y^4x^7+48y^5x^3

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(\partial)/(\partial x)(25x^8y^4+12x^4y^5)

\frac{\partial}{\partial x} (25 x^{8} y^{4} + 12 x^{4} y^{5})

200 y^{4} x^{7} + 48 y^{5} x^{3}

Solution steps

\frac{\partial}{\partial x} (25 x^{8} y^{4} + 12 x^{4} y^{5})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (25 x^{8} y^{4}) + \frac{\partial}{\partial x} (12 x^{4} y^{5})

\frac{\partial}{\partial x} (25 x^{8} y^{4}) = 200 y^{4} x^{7}

\frac{\partial}{\partial x} (12 x^{4} y^{5}) = 48 y^{5} x^{3}

= 200 y^{4} x^{7} + 48 y^{5} x^{3}

\int 5 e^{x} + cos (\frac{x}{2}) d x

2^{a r c t a n (x)}

\int (2 x - 3)^{2} d x

\frac{d}{d x} (x^{3} arctan (3 x))

3 (sin (x))^{x}

What is (\partial)/(\partial x)(25x^8y^4+12x^4y^5) ?
The answer to (\partial)/(\partial x)(25x^8y^4+12x^4y^5) is 200y^4x^7+48y^5x^3