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Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following functions at given points using the definition: at a without numerical value at a=2

Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following functions at given points using the definition: at a without numerical value at a=2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the derivatives a) f(x)=√x+1 at a without numerical value b) f(x) = sin(x+3) at a=0 c) f(x) = == X x+1 of the following functions at given points using the definition: at a=2
Transcribed Image Text:Find the derivatives a) f(x)=√x+1 at a without numerical value b) f(x) = sin(x+3) at a=0 c) f(x) = == X x+1 of the following functions at given points using the definition: at a=2
Expert Solution
Step 1

Given the functions,

(a) fx=x+1 at a without numerical value.

(b) fx=sinx+3 at a=0.

(c) fx=xx+1 at a=2.

The objective is to find the derivatives of the given functions at given points using the definition.

Formula Used :

(1) First Principle of derivative is if the limit exists and finite then,

f'(a)=limx→afx-fax-a or f'x=limh→0fx+h-fxh.

(2) limx→0sin xx=1.

(3)  sin A-sin B=2cosA+B2sinA-B2.

 

 

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