(a) Prove that L 6. f(t) dt = f(h(z))h'(z) – f(9(z))g'(z). [Hint: Rewrite the integral part using an antiderivative F of f. i.e, Use Fundamental Theorem of Calculus f(z) dz = F(b) – F(a).] (b) Find derivative of 1+ f3 dt.
(a) Prove that L 6. f(t) dt = f(h(z))h'(z) – f(9(z))g'(z). [Hint: Rewrite the integral part using an antiderivative F of f. i.e, Use Fundamental Theorem of Calculus f(z) dz = F(b) – F(a).] (b) Find derivative of 1+ f3 dt.
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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6. (a) Prove that
dz
f(t) dt = f(h(z))h'(x) – ƒ(g(x))g'(z). [Hint: Rewrite the integral part using
9(z)
an antiderivative F of f. i.e, Use Fundamental Theorem of Calculus f(x) dx = F(b) – F(a).]
(b) Find derivative of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2F68675c70-5cc2-4bc8-b38c-bfbb3ed75911%2Fzn8249p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:I
6. (a) Prove that
dz
f(t) dt = f(h(z))h'(x) – ƒ(g(x))g'(z). [Hint: Rewrite the integral part using
9(z)
an antiderivative F of f. i.e, Use Fundamental Theorem of Calculus f(x) dx = F(b) – F(a).]
(b) Find derivative of
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