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

The answer to (\partial)/(\partial x)(x^5+xy^7+6) is 5x^4+y^7

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

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

5 x^{4} + y^{7}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

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

\frac{\partial}{\partial x} (6) = 0

= 5 x^{4} + y^{7} + 0

Simplify

= 5 x^{4} + y^{7}

f (x) = 4 cos (x), (\frac{π}{3}, 2)

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

\int \frac{x e ^{3 x}}{2} d x

\int_{k}^{2 k} \frac{2}{( 2 x - k ) ^{2}} d x

What is (\partial)/(\partial x)(x^5+xy^7+6) ?
The answer to (\partial)/(\partial x)(x^5+xy^7+6) is 5x^4+y^7