What is (\partial)/(\partial x)(5x^4y^6+3x^5y^8) ?

The answer to (\partial)/(\partial x)(5x^4y^6+3x^5y^8) is 20y^6x^3+15y^8x^4

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(\partial)/(\partial x)(5x^4y^6+3x^5y^8)

\frac{\partial}{\partial x} (5 x^{4} y^{6} + 3 x^{5} y^{8})

20 y^{6} x^{3} + 15 y^{8} x^{4}

Solution steps

\frac{\partial}{\partial x} (5 x^{4} y^{6} + 3 x^{5} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{4} y^{6}) + \frac{\partial}{\partial x} (3 x^{5} y^{8})

\frac{\partial}{\partial x} (5 x^{4} y^{6}) = 20 y^{6} x^{3}

\frac{\partial}{\partial x} (3 x^{5} y^{8}) = 15 y^{8} x^{4}

= 20 y^{6} x^{3} + 15 y^{8} x^{4}

x \to 0 lim (\frac{( 6 ^{x} - 4 ^{x} )}{x})

\frac{9 x}{9 x - 5}

(y + 4) \cdot y^{^{'}} = 2 x y + 4 y

n = 0 \sum \infty (\frac{x}{2})^{n}

(2 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

What is (\partial)/(\partial x)(5x^4y^6+3x^5y^8) ?
The answer to (\partial)/(\partial x)(5x^4y^6+3x^5y^8) is 20y^6x^3+15y^8x^4