How do you find the derivative of Inverse trig function $f (x) = 7 t - 14 cos (x) + 20$ $f(x)= 7t-14cos(x)+20$ ?

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Answer 1 · 2015-10-14T02:19:14

See the explanation below.

First: there is no inverse trig function and this is not a trig function (although it involves one).

Second: Is $t$ $t$ a typing error that should be $x$ $x$ or is it another function of $x$ $x$ ?

For $f (x) = 7 t - 14 cos (x) + 20$ $f(x)= 7t-14cos(x)+20$ ,

we get use the chain rule to find $\frac{d}{d x} (7 t) = 7 \frac{d t}{d x}$ $d/dx(7t) = 7dt/dx$ ,

we use the derivative of cosine to get $\frac{d}{d x} (- 14 cos x) = - 14 (- sin x) = + 14 sin x$ $d/dx(-14cosx) = -14(-sinx) = +14sinx$ .

Therefore,

$f'(x) = 7dt/dx+14sinx$ .

For $t$ a constant, this becomes $f'(x) = 14sinx$ .

For $t=x$ , this becomes $f'(x) = 7+14sinx$ .

How do you find the derivative of Inverse trig function f(x)= 7t-14cos(x)+20f(x)=7t−14cos(x)+20f(x)= 7t-14cos(x)+20?