24.) f tan3x secx dx

Q: If y = tan-1 xy and (x = 2, y = 3) y will be equal to?

A: See the attachment

Q: Given that sec(x)=−9/2, what is sec(−x)?

A:

Q: If f(x)= tan^-1 sqrt(5x), then f'(x)= ?

A: Consider the given function. fx=tan-15x The derivative of the function is defined as,…

Q: 1. S[3 + tan(4x²)J²xdx

A:

Q: 5. Use implicit differentiation to find 8z and x² + 4y? + 92? = 8 %3D

A: 5. Some equations in x and y don't explicitly define y as a function of x. In such cases we do…

Q: 1- tanhx = sech x

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If f(x) = 7 sin-(*), then f'(2) - =

A: dsin-1xdx = 11-x2 dxndx=n.xn-1

Q: In [tan (5 + )| +o sec x dx 4 2

A:

Q: Find if, y - x = sin(xy)

A: In this question we will use differentiation property for solving this question and after that we…

Q: 11. Use the substitution u = x/3 to prove dx tan 9+x2

A: Consider the integral

Q: d (sec x) dx Prove that sec x tan x.

A: We have to prove that: ddxsec x=sec x tan x We know the formula of derivatives, dxndx=nxn-1d cos…

Q: a. Prove using the quotient rule: d sec x= sec x tan x dx

A: From the quotient rule, the derivative of the function y=uv is: dydx=vdudx-udvdxv2

Q: 7. tan' x secx dx

A:

Q: 5. Evaluate tan (x)sec'(x)dx

A: Find the integral by using substitution

Q: Prove that d/dx tan(x) = sec^2(x).

A:

Q: Find the upper bound on the error if tan (2x')~ 2x and x< 0.2 -1

A:

Q: 7. Let y = tan (3x - 2), find y'.

A:

Q: if f(x) = (sin¬'(6x + 5))', then %3D

A: Given,          fx=sin-16x+57

Q: sin x -dx 1 7/4

A:

Q: prove that  d/ dx ( sec x) =sec x tan x

A: We have to prove ddxsecx=secx tanx We know that secx=1cosx So, we have to differentiate ddx1cosx…

Q: [s sec5 x tan4x dx

A:

Q: 2/3 " tan'x sec'x dx X.

A: Solving the problem by doing the definite integral.

Q: tan(x) In(sec(x))dx

A: Consider the indefinite integral:

Q: (B) Evaluate f tan (7x +1) sec³(7x+1) dx.

A:

Q: 4. tan'x seczx dx

A: To find: The integral of ∫tan7x·sec32xdx. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C…

Q: 3. Evaluate tan¹x² 1+xº dx

A: dtan-1(x)dx=11+x2

Q: Evaluate 2. S sec*x tan*xdx

A:

Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

A:

Q: 1. Evaluate 4 (sec²x tan²x ). dx

A: Use product rule of differentiation du·vdx=vdudx+udvdx. Use chain rule of differentiation…

Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: d Use quotient rule to prove [cscx] = -cscxcotx. dx

A:

Q: d Prove that sec x tan x. sec x dx - 3.

A: Given that

Q: 1. Evaluate (sec²x tan²x ). dx

A: To find dsec2x tan2xdx Given function is y=sec2x tan2xwe know that, sec2x =1+tan2xthen…

Q: If f(x) = 7 tan'(7 sin(4x)), - f'(x) =

A: Given that, f(x) = 7tan-1[7sin (4x)] We have to find the derivative of the given function.

Q: Eliminate the arbitrary constants of: y = c1cos3x+c2sin3x+(4xcosx+sinx)/32

A: Let's find.

Q: (B) Evaluate | tan (7x +1) sec³(7x +1) dr.

A: We will use simple integration rules to solve this question.

Q: 4 (tan(sec(x)) d

A: Recall: df(g(x)dx= f'(g(x)) g'(x)     Chain Rule Differentiation d(tanx)dx =sec2x d(sec x)dx =secx…

Q: ㅠ St tan5 (2x) sec² (2x) dx

A: Given:∫π2πtan5(2x)sec2(2x)dxsubstitute u=tan(2x)differentiate on both sideswe know that…

Q: If f(x) 5 tan (7 sin(2r)), f'(x) =

A:

Q: 19. Evaluate using u-substitution: S tan6x sec² x dx

A:

Q: Compute / tan x · sec a dæ.

A: detailed solution is given below

Q: l6X-tan 3X, (- find openint & concav f(x)= 6-(seč 3x)3 3 sec?

A:

Q: Verify the identity

A: We have to prove

Q: 3. Use trigonometric substitution to evaluate Sx V9 – x² dx

A:

Q: If secA=x+1/4x ,prove that secA+tanA=2x or 1/2x

A:

Q: Find ∫sec4 3x tan3 3x dx.

A: ∫xndx=xn+1n+1+C

Q: tan³ r sec' rdr

A: The given integral is ∫0π4tan3x sec4x dx. Let u=sec x. Then du=sec x tan x. Then, the lower limit…

Q: Prove that _ d tanx = Sec'x.

A:

Q: Evaluate sec x dx /In(sec x + tan x)

A:

Q: "/3 tan5x sec²x dx

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.