What is (\partial)/(\partial x)(x^8+6xy^5) ?

The answer to (\partial)/(\partial x)(x^8+6xy^5) is 8x^7+6y^5

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(\partial)/(\partial x)(x^8+6xy^5)

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

8 x^{7} + 6 y^{5}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} + 6 y^{5}

\int 7 x^{3} cos (x^{2}) d x

x y^{^{'}} + y = 41 x

f (x) = sin^{2} (x)

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

2 - X^{2}, - X = Y

What is (\partial)/(\partial x)(x^8+6xy^5) ?
The answer to (\partial)/(\partial x)(x^8+6xy^5) is 8x^7+6y^5