EXAMPLE 1 Prove (a) cosh?(x) – sinh?(x) = 1 and (b) 1- tanh?(x) = sech?(x). %3D SOLUTION (a) cosh°(x) – sinh (x) = ( *** -(| 2 e2x + 2 + e-2x 4 4 (b) We start with the identity proved in part (a): cosh (x) – sinh (x) = 1. If we divide both sides by cosh?(x), we get 1 sinh?(x) 1 cosh?(x) 1- tanh?(x) or

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

A:

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: sinh2 (등)

A:

Q: Given that " = n, sin (x) dx 3 -T, what is 8 sin (0) de?

A:

Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: Question 5 (1 point) The derivative of y tanh(In x) is -4x Oy = x²+1 -sech? (In x) Oy = 4 Oy =…

A: The solution is given below in the next step:

Q: 3/2 x+3/2 x² - 2 Show that dx = In 3.

A: Since there are multiple questions posted, we will answer the first question posted (4). If you want…

Q: sin x 2. Find f'(x) if f(x) = 1 - cos x %3D 1 3. Simplify your result in (2) to show that f'(x) %3D…

A:

Q: 1+ sin(x) cos(r) Find the equation of the line tangent to h(r) = - You may leave your 6 at x = final…

A: Given: Curve:    hx=1+sinxcosx ory=1+sinxcosx    To find out: We need to find out the equation of…

Q: f"(x) = 5ex - 8 sin(x), (0) = 3, f(x) = 5+ 5e + 5e* + 8 sin(x) – 1

A:

Q: cos(x) = 3/6       3?/2 < x < 2? cos(x/2)=? sin(x/2)=? tan(x/2)=?

A:

Q: 21 csc' x 8. - (csc' x-1)" dx (simplify: cot' x+1= csc² x) 1 +C = tan"(x)+c ans : %3D 21 cot“ (x)

A: you can clearly understand if you follow the below solution

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

A:

Q: 1 If f(x) = sin x and f(a) = find the value of f(a) + 7f(-a). 4' -14/1 find the value of f(a) +…

A:

Q: 8(a) The functions sinh and cosh are defined as 1 sinhr=;(e-e*), coshr =1/√(₁²+ e ²). (i) Show from…

A:

Q: Question: 8 Find the first derivative for the following functions: -2x a) sin x+ cosX

A: topic - derivatives note :as per bartleby guidelines, we are supposed to answer only first question…

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

A:

Q: Example 6: Differentiate (a) y= sin(x²) (b) y =sin (x) %3D (c) y= e*cc30 (d) y=tan(4.x² –1)

A:

Q: sin?x If h (x) = | . (t² + 1) dt for – <x < 7, then h' (x) CSC 4 (A (a4 + 1) CSC B) (sinºr + 1) CSC…

A: Let's find.

Q: a3+2 arcsin(z) If f(x) = 2 cos (x) find f'(0) . FORMATTING: Your answer should be exact. Remember to…

A:

Q: J_3/2(x) = 2 TX COS X X - sin x -

A:

Q: Use the appropriate rules to differentiate two of the following: (a) y = e* cos4x (b) y= (4x² +8x)*…

A: We need to differentiate the given functions. this can be done as follows:

Q: 1-In (-) + In(2x³) = In3 %3D

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: f(x) = Answer: 1-cos(4x) 1+cos(4x) 2 sec² (2x)

A:

Q: Q\Find e* sin(x) dx О ехр (pі) O (1- exp(pi))/2 O 1+ exp(pi) O exp(pi)/2 O 1- exp(pi) O (1+…

A:

Q: Show that arctan(tanh(x)) = sech(2x). arctan(tanh(x)) dx D²tanh(x)) %3D 1 + ])-: 1/cosh²(x) 1 +…

A:

Q: ope of the curve 2xy = In(e*) sin(x)

A:

Q: True or False: In(-) ) = 2 In(x) – x – In(cos(x)) e cos(x) True O False

A: