What is (\partial)/(\partial x)(6x^7y^6+2x^5y^8) ?

The answer to (\partial)/(\partial x)(6x^7y^6+2x^5y^8) is 42y^6x^6+10y^8x^4

(\partial)/(\partial x)(6x^7y^6+2x^5y^8)

\frac{\partial}{\partial x} (6 x^{7} y^{6} + 2 x^{5} y^{8})

42 y^{6} x^{6} + 10 y^{8} x^{4}

Solution steps

\frac{\partial}{\partial x} (6 x^{7} y^{6} + 2 x^{5} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{7} y^{6}) + \frac{\partial}{\partial x} (2 x^{5} y^{8})

\frac{\partial}{\partial x} (6 x^{7} y^{6}) = 42 y^{6} x^{6}

\frac{\partial}{\partial x} (2 x^{5} y^{8}) = 10 y^{8} x^{4}

= 42 y^{6} x^{6} + 10 y^{8} x^{4}

\int sin (\frac{1}{2} x) d x

3 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 x^{2} + 7 x + 3

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

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

x \to 0 lim (\frac{a ^{x} - b ^{x}}{x})

What is (\partial)/(\partial x)(6x^7y^6+2x^5y^8) ?
The answer to (\partial)/(\partial x)(6x^7y^6+2x^5y^8) is 42y^6x^6+10y^8x^4