QUESTION 6 Find the derivative. 10 y= +6 sec x Oy'= 10 +6 tan?x O y'= - 1 - 6 cscx Cy = +6 sec x tan x 10 10 6 sec x tanx

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: cos-1 3x dx 3 – 1 – 9x2 * tan-1x dx 1+ x2 4 - n/2 5 –

A:

Q: Question 9 Find the simplified form of the derivative of y = Š Oy= 3 csc 3 CSC (3x) 3 csc 3z = cot…

A:

Q: Question 1 Find the derivative of the given function. Do not simplify your solution. y 3= (922 - 6x…

A: We have to find derivative

Q: solve all conected Question 3: Find the equation of the tangent line to the curve at the given…

A:

Q: Use..U. substitution. to. find each antiderivative. -48x 5-3x4 dx -3-

A: *to find:- integral value of the given function using substitution method.

Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

Q: Question 3 Determine the derivative of In(csc x) cot x Csc I - cot x CS z Previous

A: A detailed solution is given below

Q: 5cos3(x) Гу 3 sin(3–2x) + tan? (3x? — 4х) — csc(/2x — 1

A: Differentiate y w.r.t x.

Q: Question 1 Find the derivative and simplify y cotVt-1 Oy-- Oy= - 2tt-1 1 2t/t-1

A:

Q: . h(x)= cot 1 -tanx

A: Given:hx=cot-11x-tan-1x

Q: Question 27 Determine the second derivative of 6 y - xy2= 1 A y " = 2y³ ( 6 – 2 x y ) -2 ( 2 – x y (…

A:

Q: Question:4 Calculate by implicit derivatives (tan x)" + ycotx + sinxy – exy – In2 = 0 - dx

A: The given function is tanxy+ycotx+sinxy-exy-ln2=0 Now, we find the derivative of each term…

Q: Question 6 Find the derivative of the function y = 8ln(cos 2x)+ 5tan? (3x) Write the value of y' (0)…

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Q: Find the derivative of the trigonometric function.

A: The given function is y=31-sinx2cosx

Q: Find the derivative of cos-¹(sin x)

A:

Q: QUESTION 11 Find the derivative of the function at the given point in the direction of A. f(x, y) =…

A:

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: Find the value of the following mplicit derivative tan y-sec x=5 find...y'

A: Given query is to find the derivative of the expression.

Q: QUESTION 5 Find the derivative. y%3= + 8 sec x Oy'-2- 8 sec x tan x x2 Oy'- - 7. +8 sec x tan x Oy'=…

A:

Q: 1) tan x Find the derivative of y= = e

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Q: 83. Find the 50th derivative of y = cos 2x.

A:

Q: 28) y = tan² 2 29) y = In ln x 30) y = (x In æ)²

A:

Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

A:

Q: Find the first derivative Complete Solution.  1.) t=sinθtanθ

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Q: What is the derivative of 0.50 sin 2t+0.30 cos t

A:

Q: Question 2 Let a be a real valued constant. Find the derivative with respect to x: Y = 4ae 1-4ae4z O…

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Q: 1-cos 4x Find the derivative of y sin 4x

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Q: Part 1 Find the equation of the tangent line to the curve a(x) = 3 sin x+In(x2 - 5x +1) – e-6z at a…

A:

Q: Cos 4x S cos 2x-sin 2x dx

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: 8e cos 2x dx csc(x) sec(x)

A:

Q: QUESTION 4 Find the derivative. y =x 5/6 Os,5/6 x1/6 1/5 Ox-1/6

A: Note that  d/dx (x^n) = nx^(n-1)

Q: Question 6 Consider the function below: sin(x²+y) { (x, y) # (0,0) (x, y) = (0,0) f(æ, y) y-x Find…

A:

Q: Question 3 Determine the derivative of ln(csc x) - cot x CSC I O csc x cot x

A:

Q: Question 12. Obtain the derivative of the function f(x) = sin(6x – 8) Enter the answer as a function…

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Q: Solve the second derivative ду? for f(x) = tan-1

A: the given function f(x)=tan-1x2y2to find ∂2f∂y2

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: Question 2: Compute the derivative of y = arcsin(cos(arctan(r))).

A:

Q: Find the derivative of the given function:

A:

Q: Question 10 Calculate the second derivative of the function y= In(cosx). -csc2x -sec?x c) cscx D)…

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Q: y = [x + (x + sin² x)³]4 I

A:

Q: Question 16 O [CLO-2] Find the derivative of f(x)=tan -¹ (√2x) O √√2x+√√88² (1+√√2x)² 1 √√√2x+√√2x³

A:

Q: 5. S sin5x cos 3x dx

A:

Q: Question 26 Calculate the second derivative of the function y = In(cosx). A -sec'x B) -csc2x csc?x…

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Q: Find the derivatives of the functions r = 6(sec θ - tan θ)3/2

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Q: Find the first derivatives of y = 2 tan?x - sec?x

A:

Q: Question 12 VI² – 1 What is the derivative of y O y = 1 1 - 1 O y' %3| 22-1 O y' =

A: Given query is to find the derivative of the expression.

Q: Question 1: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the…

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Q: Find the first derivative of the function y = In[tan (pi/4 + x/2)

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Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: