What is (\partial)/(\partial x)(3e^y+x+x^3+6) ?

The answer to (\partial)/(\partial x)(3e^y+x+x^3+6) is 3x^2+1

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(\partial)/(\partial x)(3e^y+x+x^3+6)

\frac{\partial}{\partial x} (3 e^{y} + x + x^{3} + 6)

3 x^{2} + 1

Solution steps

\frac{\partial}{\partial x} (3 e^{y} + x + x^{3} + 6)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 e^{y}) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (6)

\frac{\partial}{\partial x} (3 e^{y}) = 0

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

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

= 0 + 1 + 3 x^{2} + 0

Simplify

= 3 x^{2} + 1

y^{^{'}} = 2 x y^{2}

f (x) = 7 e^{x}

\frac{d}{d x} (\frac{4 b}{a} x a^{2} - x^{2})

j o in 1 - 4 x + f (x)

d er i v a t i v e y = (arctan (x))^{2}

What is (\partial)/(\partial x)(3e^y+x+x^3+6) ?
The answer to (\partial)/(\partial x)(3e^y+x+x^3+6) is 3x^2+1