Use part I of the Fundamental Theorem of Calculus to find the derivative of f(2) = ], 14F° 1 dt 1+t3

Trigonometry (MindTap Course List)
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ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Use part I of the Fundamental Theorem of Calculus to find the derivative of
5(<) = [ E
1
dt
1+ t3
Transcribed Image Text:Use part I of the Fundamental Theorem of Calculus to find the derivative of 5(<) = [ E 1 dt 1+ t3
1
dr is
The value of
00
Transcribed Image Text:1 dr is The value of 00
Expert Solution
Step 1

Given

f(x) = 2x11+t3dt

First fundamental theorem: if  F(x) is continuous on [a,b] and f(x) is differentiable function on(a.b) then

ddxf(x) =ddx axF(t)dt=F'(x)

 

Step 2

By the fundamental theorem of calculus

ddxf(x) = ddx2x11+t3dtddxf(x) = 11+x3

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