What is (\partial)/(\partial x)(x^5+x^2y+x+5) ?

The answer to (\partial)/(\partial x)(x^5+x^2y+x+5) is 5x^4+2xy+1

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(\partial)/(\partial x)(x^5+x^2y+x+5)

\frac{\partial}{\partial x} (x^{5} + x^{2} y + x + 5)

5 x^{4} + 2 x y + 1

Solution steps

\frac{\partial}{\partial x} (x^{5} + x^{2} y + x + 5)

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^{2} y) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (5)

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 5 x^{4} + 2 y x + 1 + 0

Simplify

= 5 x^{4} + 2 x y + 1

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = 3

x \to 1 lim (e^{x^{2} - 4 x + 1})

\int sin (in x) d x

\int_{- 1}^{0} 1

\int e^{\frac{x}{y}} d x

What is (\partial)/(\partial x)(x^5+x^2y+x+5) ?
The answer to (\partial)/(\partial x)(x^5+x^2y+x+5) is 5x^4+2xy+1