How do you find the derivative of $5^{tan x}$ $5^tanx$ ?

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Answer 1 · 2016-11-30T18:42:28

$\frac{d}{d x} (5^{tan x}) = (5^{tan x}) \cdot ln 5 \cdot {sec}^{2} x$ $d/dx(5^(tan x))=(5^tan x)*ln 5*sec^2 x$

The formula to differentiate is

$\frac{d}{d x} (a^{u}) = a^{u} \cdot ln a \cdot \frac{d}{d x} (u)$ $d/dx(a^u)=a^u*ln a*d/dx(u)$

therefore

$\frac{d}{d x} (5^{tan x}) = 5^{tan x} \cdot ln 5 \cdot \frac{d}{d x} (tan x)$ $d/dx(5^tan x)=5^tanx*ln 5*d/dx(tan x)$

$\frac{d}{d x} (5^{tan x}) = 5^{tan x} \cdot ln 5 \cdot {sec}^{2} x \cdot (\frac{d x}{d x})$ $d/dx(5^tan x)=5^tanx*ln 5*sec^2 x*(dx/dx)$

$\frac{d}{d x} (5^{tan x}) = (5^{tan x}) \cdot ln 5 \cdot {sec}^{2} x$ $d/dx(5^(tan x))=(5^tan x)*ln 5*sec^2 x$

God bless....I hope the explanation is useful.

How do you find the derivative of 5tanx5^tanx?