2. Find the third order derivative of y = In(secx + tan x). a. secx b. secx tan x c. - sec(x) + 2 sec³ x - secx+6 sec"x d. cotx

Q: find the derivatives of both: y = sec2(x) − tan2(x)   y = x3 cot(x)

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: find the derivative of y with respect to the appropriate variable. 1. y = cos-1 (x2)   2. y =…

A: Part 1. Given,

Q: Find the derivative of y = (tan x)cos: COs x .

A: Given : y=(tanx)cosx

Q: Find the derivative of the function.

A: To Find the derivative of the function. y = ln sec x + tan x

Q: Use the chain rule to find the derivative of the function z = x2y3 − x along the curve given by x =…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

A:

Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 5s

A:

Q: Evaluate the derivative of the function. y= sec "(2 In 8x) dx

A:

Q: Use forward-difference formula to evaluate the first derivative of y = tan(x) at x = 1 using a value…

A: The two-point forward difference formula to calculate f'(x) is f'(x)=f(x+h)-f(x)h, where h is the…

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

A:

Q: find the derivative of y with respect to the appropriate variable 19. y = (sech u)(1 - ln sech u)…

A: Hello! Thank you for your question. We’ll answer the first question since the exact one wasn’t…

Q: Use forward-difference formula to evaluate the first derivative of y = sin(x) at x = O 2√2 π -2√2 ㅠ…

A: Given that y=sinx. We have to find the first derivative of y=sinx at x=π2 using a value of h=π4 by…

Q: 14) The derivative of y = cscx sin x is y = 0 A) True B) False

A:

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

A:

Q: , find the derivative of y with respect to the appropriate variable 21. y = ln cosh y - 1/2 tanh2 y…

A: (21) Consider the provided equation, y=lncoshy-12tanh2y Find the derivative of y with respect to the…

Q: Find the derivative with respect to x: y = tan(Vx2 – 1) + csc-(x),x > 1

A:

Q: find the derivative of y with respect to the appropriatevariable. y = (sech θ)(1 - ln sechθ)

A: We have to take derivative with respect to θ. dydθ=sinh θ ddθ1-ln sech θ+1-ln sech θddθsinh θ

Q: Obtain the derivative of the function y (3 sen(4x))° ( tgʻ(2x)) y = (sec(2x))* – 1

A: This question is based on Trignometric application and diffrentiation of function.

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

A:

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: 17. Find the first derivative for J(x)=tan0x sec0

A:

Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec" 27) y = -sin-1 (5x2 + 2) 28) y =…

A:

Q: Find the derivative of y = In (tanh x).

A:

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: Find the derivative of the function by using the chain rule. sinx (a) h(x) = tan(x³ sinx) (b) y= %3D…

A: To find the derivative of the given function using the chain rule, which is:…

Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

A:

Q: Compute the derivative of the function y = 6 cos- (7x) at the point x = (Use symbolic notation and…

A:

Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

A:

Q: tan (2x) 3. y = sin (5x–1)

A:

Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: 3/ By using the definition of derivative, proof that tan x = sec? x. %3D dx

A: By definition of derivative , f'(x) = d(f(x)dx= limh→0f(x+h) - f(x)h L Hosital's Rule :When limit is…

Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

A:

Q: sinx (a) h(x) = tan(x² sin.x) (b) y= V1+cos.x

A:

Q: 5. Find the derivative of h(x) = cos(sin(cosx)).

A:

Q: 2x Find the second order derivative of y = Tan 1-x

A:

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: Find the derivative of y with respect to x. 26) y = sec-1|2x+3 5 26) y = sec

A: We find the derivative using the chain rule

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Find the derivative of y with respect to x.   y= tan-1 *square root (16x2-1) +csc-1*4x ,   x greater…

A:

Q: Use three-point midpoint formula to evaluate the first derivative of y = sin(x) at x = using a value…

A: To find- Use three-point midpoint formula to evaluate the first derivative of y = sinx at x = π2…

Q: Obtain the derivative of the function y cos (9y ) + tan (4x) csc (2x) y =

A: