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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

State the derivative of each function.

(a) y = xn

(b) y = ex

(c) y = bx

(d) y = ln x

(e) y = log x

(f) y =sin x

(g) y = cos x

(h) y = tan x

(i) y = csc x

(j) y=sec x

(k)y=cot x

(l) y =sin–1x

(m) y = cos–1x

(n) y = tan–1x

(o) y = sinh x

(p) y = cosh x

(q) y = tanh x

(r) y = sinh–1x

(s) y = cosh–1x

(t) y = tanh–1x

(a)

To determine

To State: The derivative of y=xn.

Explanation

Binomial expansion:

(x+h)n=xn+nxn1h+n(n1)2xn2h2+...+nxhn1+hn

Calculation:

Obtain the derivative of y.

y=limh0(x+h)nxnh=limh0(xn+nxn1h+n(n1)2xn2h2+

(b)

To determine

To find: The derivative of y=ex.

(c)

To determine

To find: The derivative of y=bx.

(d)

To determine

To find: The derivative of y=lnx.

(e)

To determine

To find: The derivative of y=logbx.

(f)

To determine

To find: The derivative of y=sinx.

(g)

To determine

To find: The derivative of y=cosx.

(h)

To determine

To find: The derivative of y=tanx.

(i)

To determine

To find: The derivative of y=cscx.

(j)

To determine

To find: The derivative of y=secx.

(k)

To determine

To find: The derivative of y=cotx.

(l)

To determine

To find: The derivative of y=sin1x.

(m)

To determine

To find: The derivative of y=cos1x.

(n)

To determine

To find: The derivative of y=tan1x.

(o)

To determine

To find: The derivative of y=sinhx.

(p)

To determine

To find: The derivative of y=coshx.

(q)

To determine

To find: The derivative of y=tanhx.

(r)

To determine

To find: The derivative of y=sinh1x.

(s)

To determine

To find: The derivative of y=cosh1x.

(t)

To determine

To find: The derivative of y=tanh1x.

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