What is (\partial)/(\partial x)(e^y+x+x^4+5) ?

The answer to (\partial)/(\partial x)(e^y+x+x^4+5) is 4x^3+1

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(\partial)/(\partial x)(e^y+x+x^4+5)

\frac{\partial}{\partial x} (e^{y} + x + x^{4} + 5)

4 x^{3} + 1

Solution steps

\frac{\partial}{\partial x} (e^{y} + x + x^{4} + 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (e^{y}) = 0

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

= 0 + 1 + 4 x^{3} + 0

Simplify

= 4 x^{3} + 1

5 + 2 x, \frac{( 15 + x )}{3}

\frac{\partial}{\partial x} (2 x^{2} y + 4 y^{3})

y = (x + \frac{1}{x}) (x - \frac{1}{x} + 1)

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

\frac{d}{d x} (2 ln (x))

What is (\partial)/(\partial x)(e^y+x+x^4+5) ?
The answer to (\partial)/(\partial x)(e^y+x+x^4+5) is 4x^3+1