Gennaio 20, 2020

di Rasia

Qual è la derivata di ${tan}^{2} x$ $tan ^ 2 x$ ?

Risposta:

$2 tan x {sec}^{2} x$ $2tanxsec^2x$

Spiegazione:

$note {tan}^{2} x = {(tan x)}^{2}$ $"note "tan^2x=(tanx)^2$

$differentiate using the chain rule$ $"differentiate using the "color(blue)"chain rule"$

$given y = f (g (x)) then$ $"given "y=f(g(x))" then"$

$\frac{d y}{d x} = f' (g (x)) \times g' (x) \leftarrow chain rule$ $dy/dx=f'(g(x))xxg'(x)larr" chain rule"$

$y = {(tan x)}^{2}$ $"y=(tanx)^2$

$\Rightarrow \frac{d y}{d x} = 2 tan x \times \frac{d}{d x} (tan x)$ $rArrdy/dx=2tanx xxd/dx(tanx)$

$\Rightarrow \frac{d y}{d x} = 2 tan x {sec}^{2} x$ $color(white)(rArrdy/dx)=2tanxsec^2x$

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