What is (\partial)/(\partial x)(x^8+2xy^7) ?

The answer to (\partial)/(\partial x)(x^8+2xy^7) is 8x^7+2y^7

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(\partial)/(\partial x)(x^8+2xy^7)

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

8 x^{7} + 2 y^{7}

Solution steps

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

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

\frac{\partial}{\partial x} (2 x y^{7}) = 2 y^{7}

= 8 x^{7} + 2 y^{7}

t^{4} - 8 t^{3} + 1 0^{2}

2 cos (5 t)

y = e^{x}, y = e^{- x}, 0, 4

\frac{x - 1}{2 - x}

x \to 1 + lim (5 - x^{2})

What is (\partial)/(\partial x)(x^8+2xy^7) ?
The answer to (\partial)/(\partial x)(x^8+2xy^7) is 8x^7+2y^7