What is the derivative of (x+2)^{2^'} ?

The derivative of (x+2)^{2^'} is 2^'(x+2)^{2^'-1}

What is the first derivative of (x+2)^{2^'} ?

The first derivative of (x+2)^{2^'} is 2^'(x+2)^{2^'-1}

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derivative of

(x + 2)^{2^{^{'}}}

2^{'} (x + 2)^{2^{'} - 1}

Solution steps

\frac{d}{d x} ((x + 2)^{2^{^{'}}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x + 2)^{2^{^{'}}} = e^{2^{^{'}} l n (x + 2)}

= \frac{d}{d x} (e^{2^{^{^{'}}} l n (x + 2)})

Apply the chain rule:

e^{2^{^{'}} l n (x + 2)} \frac{d}{d x} (2^{^{'}} ln (x + 2))

= e^{2^{^{'}} l n (x + 2)} \frac{d}{d x} (2^{^{'}} ln (x + 2))

\frac{d}{d x} (2^{^{'}} ln (x + 2)) = \frac{2 ^{^{'}}}{x + 2}

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

Simplify

e^{2^{^{'}} l n (x + 2)} \frac{2 ^{^{'}}}{x + 2} : 2^{^{'}} (x + 2)^{2^{^{'}} - 1}

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

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\frac{d}{d x} (\frac{2 x ^{5}}{5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4})

z \to 0 lim ((2 z - 8) \frac{1}{3})

\frac{d}{d x} ((3 x + 5)^{2})

What is the derivative of (x+2)^{2^'} ?
The derivative of (x+2)^{2^'} is 2^'(x+2)^{2^'-1}
What is the first derivative of (x+2)^{2^'} ?
The first derivative of (x+2)^{2^'} is 2^'(x+2)^{2^'-1}