Determine the second derivative of q (t ) = sec (5t ), Mathematics

Assignment Help:

Determine the second derivative for following functions.

                            Q (t ) = sec (5t )

Solution : Following is the first derivative.

             Q′ (t ) = 5 sec (5t ) tan (5t )

 Notice as well that the second derivative will require the product rule now.

Q′′ (t ) = 25 sec (5t ) tan (5t ) tan (5t ) + 25 sec (5t ) sec2 (5t )

            = 25 sec (5t ) tan 2 (5t ) + 25 sec3 (5t )

Notice  as well that each successive derivative will needs a product and/or chain rule & that as noted above it will not ending up returning back to only a secant after four (or another other number for that matter) derivatives as sine & cosine will.

 As we saw previously we will frequently need to utilize the product or quotient rule for the higher order derivatives, even while the first derivative didn't need these rules.

Let's work one more instance that will see how to utilize implicit differentiation to determine higher order derivatives.

 


Related Discussions:- Determine the second derivative of q (t ) = sec (5t )

Circles, Two tangents TP and TQ are drawn to a circle with center O from an...

Two tangents TP and TQ are drawn to a circle with center O from an external point T.prove that angle PTQ=angle 2 OPQ

Introduction to multiplication and division, INTRODUCTION :  When a Class ...

INTRODUCTION :  When a Class 5 child was given the problem 'If I paid Rs. 60 for 30 pencil boxes, how much did b pencil box cost?', he said it would be 60 x 30 = 1800. This

Geometry, I need help in my homework

I need help in my homework

Build an equation for a hyperboloid of two sheets, 1. Build an equation for...

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

Shares and dividend, A man in rested rupee 800 is buying rupee5 shares and ...

A man in rested rupee 800 is buying rupee5 shares and then they are selling at premium of rupee 1.15.he sells all the share.find profit?

Subspace of r containing n, Give an example of each of the following given ...

Give an example of each of the following given below . You do not require to give any justi cation. (a) A nonempty, bounded subset of Q with no in mum in Q. (b) A subspace of

Graphs, the value of y for which x=-1.5

the value of y for which x=-1.5

Find fourier series, Question: Find Fourier series for the periodic fun...

Question: Find Fourier series for the periodic function of period 2 π,defined by      f(x) = x 4 ,  - π ≤ x ≤ π

Concepts of sampling error, Use the concepts of sampling error and z- scor...

Use the concepts of sampling error and z- scores to explain the concept of distribution of sample means.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd