Mathematics, 27.12.2021 02:10 georgehall9515
Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a correct process for finding h' (x) ?
Answers: 3
![\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''](/tpl/images/2606/2332/88bc9.png)
![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](/tpl/images/2606/2332/9c114.png)
![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](/tpl/images/2606/2332/fb0e0.png)
![\displaystyle h(x) = [2 + f(\sin x)]''](/tpl/images/2606/2332/525da.png)
![\displaystyle h'(x) = [2 + f(\sin x)]''' [2 + f(\sin x)]'](/tpl/images/2606/2332/c90ef.png)
Rewrite [Derivative Property - Addition/Subtraction]: ![\displaystyle h'(x) = [2 + f(\sin x)]''' \bigg[(2)' + [f(\sin x)]' \bigg]](/tpl/images/2606/2332/fe368.png)
Derivative Rule [Basic Power Rule]: ![\displaystyle h'(x) = [2 + f(\sin x)]''' [f(\sin x)]'](/tpl/images/2606/2332/8ea2a.png)
Derivative Rule [Chain Rule]: ![\displaystyle h'(x) = [2 + f(\sin x)]''' f'(\sin x)(\sin x)'](/tpl/images/2606/2332/929e7.png)
Trigonometric Differentiation: 
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Let f be a differentiable function. If h (x) = (2+ f (sin x))", which of the following gives a corre...
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