Let u 1 , u 2 , u 3 , υ 1 , υ 2 , υ 3 , w 1 , w 2 , and w 3 , be differentiable functions of t . Use Exercise 54 to show that d d t u 1 u 2 u 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 = u ′ 1 u ′ 2 u ′ 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ ′ 1 υ ′ 2 υ ′ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ 1 υ 2 υ 3 w ′ 1 w ′ 2 w ′ 3
Let u 1 , u 2 , u 3 , υ 1 , υ 2 , υ 3 , w 1 , w 2 , and w 3 , be differentiable functions of t . Use Exercise 54 to show that d d t u 1 u 2 u 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 = u ′ 1 u ′ 2 u ′ 3 υ 1 υ 2 υ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ ′ 1 υ ′ 2 υ ′ 3 w 1 w 2 w 3 + u 1 u 2 u 3 υ 1 υ 2 υ 3 w ′ 1 w ′ 2 w ′ 3
Let
u
1
,
u
2
,
u
3
,
υ
1
,
υ
2
,
υ
3
,
w
1
,
w
2
,
and
w
3
,
be differentiable functions of t. Use Exercise 54 to show that
d
d
t
u
1
u
2
u
3
υ
1
υ
2
υ
3
w
1
w
2
w
3
=
u
′
1
u
′
2
u
′
3
υ
1
υ
2
υ
3
w
1
w
2
w
3
+
u
1
u
2
u
3
υ
′
1
υ
′
2
υ
′
3
w
1
w
2
w
3
+
u
1
u
2
u
3
υ
1
υ
2
υ
3
w
′
1
w
′
2
w
′
3
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
4.1 Basic Rules of Differentiation.
1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with
appropriate derivative notation.
a) y=8x-5x3 4
X
b)
y=-50 √x+11x
-5
c) p(x)=-10x²+6x3³
Please refer below
For the following function f and real number a,
a. find the slope of the tangent line mtan
=
f' (a), and
b. find the equation of the tangent line to f at x = a.
f(x)=
2
=
a = 2
x2
a. Slope:
b. Equation of tangent line: y
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage