What is the derivative of 1/20 e^x+x^6-x^e+e ?

The derivative of 1/20 e^x+x^6-x^e+e is 6x^5-ex^{e-1}+1/20 e^x

What is the first derivative of 1/20 e^x+x^6-x^e+e ?

The first derivative of 1/20 e^x+x^6-x^e+e is 6x^5-ex^{e-1}+1/20 e^x

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\frac{d}{d x} (\frac{1}{20} e^{x} + x^{6} - x^{e} + e)

6 x^{5} - e x^{e - 1} + \frac{1}{20} e^{x}

Solution steps

\frac{d}{d x} (\frac{1}{20} e^{x} + x^{6} - x^{e} + e)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{20} e^{x}) + \frac{d}{d x} (x^{6}) - \frac{d}{d x} (x^{e}) + \frac{d e}{d x}

\frac{d}{d x} (\frac{1}{20} e^{x}) = \frac{1}{20} e^{x}

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

\frac{d}{d x} (x^{e}) = e x^{e - 1}

\frac{d e}{d x} = 0

= \frac{1}{20} e^{x} + 6 x^{5} - e x^{e - 1} + 0

Simplify

= 6 x^{5} - e x^{e - 1} + \frac{1}{20} e^{x}

\frac{\partial}{\partial x} (sin^{9} (x))

\frac{\partial}{\partial y} (y \cdot cos (y - 2 x))

f (x) = x^{2} - x + 1

x \to 0 lim (x^{3})

\frac{d}{d x} ((3 x^{2} + 3 x - 1)^{4})

What is the derivative of 1/20 e^x+x^6-x^e+e ?
The derivative of 1/20 e^x+x^6-x^e+e is 6x^5-ex^{e-1}+1/20 e^x
What is the first derivative of 1/20 e^x+x^6-x^e+e ?
The first derivative of 1/20 e^x+x^6-x^e+e is 6x^5-ex^{e-1}+1/20 e^x