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

Answer 1

Luke Alvarez

See the explanation below.

First off, even though it uses one, this is not a trig function and there is no inverse trig function.

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

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

we get use the chain rule to find #d/dx(7t) = 7dt/dx#,

we use the derivative of cosine to get #d/dx(-14cosx) = -14(-sinx) = +14sinx#.

Consequently,

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

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

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

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Answer 2

Evelyn Agard

To find the derivative of the inverse trigonometric function ( f(x) = 7t - 14\cos(x) + 20 ), we apply the chain rule. The derivative of an inverse trigonometric function is given by (\frac{d}{dx}(\arccos(u)) = -\frac{1}{\sqrt{1-u^2}} \cdot \frac{du}{dx}), where ( u = \cos(x) ). Then, we differentiate ( u ) with respect to ( x ) and substitute it into the derivative expression.

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Answer from HIX Tutor

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