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9 Nov 2018

3. Find the derivative of each function. a) f(x) = x b) g(x) = sec(z sinh ) c) h(x) = [ * sint di

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Patrina Schowalter
Patrina SchowalterLv2
10 Nov 2018

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3. Find the derivative of the following functions. (a) f(x) = x Inc (b) g(x) = V1 – sin²x sec(22 + x) (c) h() = 3e21 +1

8. (a) Show that sinh-1 = ln(x + x2 + 1) Solution: Let y = sinh? 1. Then, 2 ev-e-y T = sinh y = - 2x = -e-y 0 = (eu)2 – 2xe" - 1 Then, by the Quadratic Formula we get 2x + e = - 4r2 + 4 -=IV2+1 2 Since, e > 0 we must have e = 1 + x2 +1 and so y=In(x + Vr2+1) [2] (b) Show that if f(x) = sinh-, then f'(x) = vez Solution: Using our answer from part (a) we get f(a) = + Ver #1 (1+ 2vmti) - z+Ve+I (+229 ) VEHI 1 =- 1 r2+1 x2 +1+1 Vr2 +1 I+ r2+1

1 2. (a) Find the tangent line to the graph of s(2)=x+ when r = 1. (b) Find the derivative of p(x) = (ln(5.c) + )(2-3V ). (c) Find the derivative of j(x) = 60(2*+52) (d) Find the derivative of k(2) = (e) The following table gives some values for f(x), f'(x), g(x), and g'(x). | f(x) | 3|1|2|2 f'(x) | 1 46 | 4 g(1) 0-183 () -2 0 4-1 • Let h(x) = f(t)g(2). Find h' (6). • Let r(x) = f(g(x)). Find /'6).

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