What is (\partial)/(\partial x)(x^6+xy^5+7) ?

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

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(\partial)/(\partial x)(x^6+xy^5+7)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (7) = 0

= 6 x^{5} + y^{5} + 0

Simplify

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

\int (cos (x) + x cos (y) - y) d y

(6 + x) y^{^{'}} = 7 y

\int \frac{3}{18 + 2 t ^{2}} d t

\frac{d}{d x} (cos (t) i)

x \to 1 lim (30)

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