What is (\partial)/(\partial x)(x^8+6xy^7) ?

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

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(\partial)/(\partial x)(x^8+6xy^7)

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

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

Solution steps

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

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^{7})

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

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

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

6 + \frac{1}{x ^{2}}

y^{^{''}} + 4 y = 3 cos (2 t) - 5 sin (2 t)

y = x^{4} - 4 x^{2} + 10, at x = 1

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

\int_{0}^{1} \frac{x}{1 - x ^{2}} d x

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