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

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

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

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

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

Solution steps

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

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

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

\frac{\partial}{\partial x} (5) = 0

= 8 x^{7} + y^{5} + 0

Simplify

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

d er i v a t i v e y = 2 (6 x^{9} - 10 x + 4)^{- 3}

x \to \infty lim (e^{3})

d er i v a t i v e f (x) = (x + \frac{1}{x})^{5}

\int_{30}^{150} \frac{75}{2 x ^{2}} d x

in v erse l a pl a ce \frac{s - 5}{s ^{2} + s - 6}

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