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(a) nd the es ol (i) y = tan-¹(x - √1+x²) (ii) y = x sin¹x + √1_x² (iii) f(x) = arccos(√) (iv) f(x) = ecosh z (v) f(z)= tanh '(sinx) (b) Use the definition of the derivative to prove that lim my whilele po In(1+x) I

(a) nd the es ol (i) y = tan-¹(x - √1+x²) (ii) y = x sin¹x + √1_x² (iii) f(x) = arccos(√) (iv) f(x) = ecosh z (v) f(z)= tanh '(sinx) (b) Use the definition of the derivative to prove that lim my whilele po In(1+x) I

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Find the derivatives of the following functions. Simplify where poss (i) y = tan ¹(x - √1+x²) (ii) y = x sin¯¹ x + √I (iii) f(x) = arccos(√T) (iv) f(x) = e cosh z (v) f(z) = tanh '(sing) (b) Use the definition of the derivative to prove that x2 lim ln(1 + x) I
Transcribed Image Text:(a) Find the derivatives of the following functions. Simplify where poss (i) y = tan ¹(x - √1+x²) (ii) y = x sin¯¹ x + √I (iii) f(x) = arccos(√T) (iv) f(x) = e cosh z (v) f(z) = tanh '(sing) (b) Use the definition of the derivative to prove that x2 lim ln(1 + x) I
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