What is the (((1+e^x)/2)^9)^' ?

The (((1+e^x)/2)^9)^' is (9e^x(1+e^x)^8)/(512)

What is the first (((1+e^x)/2)^9)^' ?

The first (((1+e^x)/2)^9)^' is (9e^x(1+e^x)^8)/(512)

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((\frac{1 + e ^{x}}{2})^{9})^{^{'}}

\frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}

Solution steps

((\frac{1 + e ^{x}}{2})^{9})^{'}

Apply the chain rule:

9 (\frac{1 + e ^{x}}{2})^{8} (\frac{1 + e ^{x}}{2})^{'}

= 9 (\frac{1 + e ^{x}}{2})^{8} (\frac{1 + e ^{x}}{2})^{'}

(\frac{1 + e ^{x}}{2})^{'} = \frac{1}{2} e^{x}

= 9 (\frac{1 + e ^{x}}{2})^{8} \frac{1}{2} e^{x}

Simplify

9 (\frac{1 + e ^{x}}{2})^{8} \frac{1}{2} e^{x} : \frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}

= \frac{9 e ^{x} ( 1 + e ^{x} ) ^{8}}{512}

What is the (((1+e^x)/2)^9)^' ?
The (((1+e^x)/2)^9)^' is (9e^x(1+e^x)^8)/(512)
What is the first (((1+e^x)/2)^9)^' ?
The first (((1+e^x)/2)^9)^' is (9e^x(1+e^x)^8)/(512)