if f(x) = 2^tanx then f'(pi/4)

Identify Function and Point: Step 1: Identify the function and the point of interest. We have the function f(x) = 2^tan(x) and we need to find its derivative at x = π/4.Apply Chain Rule: Step 2: Use the chain rule to differentiate f(x). f'(x) = 2^tan(x) * ln(2) * sec^2(x)Substitute x Value: Step 3: Substitute x = π/4 into the derivative. f'(π/4) = 2^tan(π/4) * ln(2) * sec^2(π/4)Calculate Trigonometric Functions: Step 4: Calculate tan(π/4) and sec^2(π/4). tan(π/4) = 1, sec(π/4) = √2, so sec^2(π/4) = 2.Final Derivative Calculation: Step 5: Substitute these values into the derivative. f'(π/4) = 2^1 * ln(2) * 2 = 2 * ln(2) * 2 = 4ln(2)

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if $f(x) = 2^{\tan(x)}$ then $f'(\frac{\pi}{4})$

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Algebra 2

Evaluate expression when two complex numbers are given

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Q. if

f(x) = 2^{\tan(x)}

then

f'(\frac{\pi}{4})

Identify Function and Point: Step $1$ : Identify the function and the point of interest. $\newline$ We have the function $f(x) = 2^{\tan(x)}$ and we need to find its derivative at $x = \frac{\pi}{4}$ .
Apply Chain Rule: Step $2$ : Use the chain rule to differentiate $f(x)$ . $f'(x) = 2^{\tan(x)} \cdot \ln(2) \cdot \sec^2(x)$
Substitute x Value: Step $3$ : Substitute $x = \frac{\pi}{4}$ into the derivative. $f'(\frac{\pi}{4}) = 2^{\tan(\frac{\pi}{4})} \cdot \ln(2) \cdot \sec^2(\frac{\pi}{4})$
Calculate Trigonometric Functions: Step $4$ : Calculate $\tan(\pi/4)$ and $\sec^2(\pi/4)$ . $\newline$ $\tan(\pi/4) = 1$ , $\sec(\pi/4) = \sqrt{2}$ , so $\sec^2(\pi/4) = 2$ .
Final Derivative Calculation: Step $5$ : Substitute these values into the derivative. $\newline$ $f'(\frac{\pi}{4}) = 2^1 \times \ln(2) \times 2$ $\newline$ $= 2 \times \ln(2) \times 2$ $\newline$ $= 4\ln(2)$