Compute / tan x · sec a dæ.

Q: Determine f sin x sin(cos x) dx

A: We have to solve the problem

Q: aluate 4e3 tan z sec2 x dx.

A:

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: y = tan* (sin æ)

A: Herewe have to do derivative of the given function.

Q: Evaluate esin(x) cos(x)dx

A: Given: I=∫esinxcosxdx for evaluating given integral, in given integral we substitute esinx=t…

Q: Find integral.

A: To Determine: ∫ e-xtane-xdx

Q: Find y= tan' ( ) Sin Sa ® y= Sin" (x) ® y= log, [tanx]

A: We use the following methods to calculate differentiate d/dx of tan inverse x =1/1+x²  d/dx of sin…

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: Derive a formula for the equation below: tan x sec" x dx Where n + 0

A:

Q: Differentiate the function y=sin^2 x

A: Given: y=sin2(x)

Q: S tan ( – y) dy 4

A: ∫tany4-y dy=∫tany-4y4 dy=∫tan-3y4 dy Now put, -3y4=t⇒-341=dtdy⇒dy=-43dt

Q: evaluate the integral.

A:

Q: (B) Evaluate tan (5x +1) sec³(5x +1) dx

A: We have to evaluate the integral.

Q: Hw)if J-0-Gso and X=e+Case Show thnt Sece+tan 0

A:

Q: (B) Evaluate tan (5x +1) sec³(5x+1) dx

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: y = cos (arcsin væ) + sin ( arccos 2

A:

Q: Find if y = sin /- cos r and r= 1+ cos-x %3D dx

A:

Q: Using an appropriate substitution, S tan (x)sec (x)dx is equal to:

A: Given∫tan3(x)sec9(x)dx

Q: tan (t) dt. cos (t)

A:

Q: rind if, y² + x² = sin(xy) using implicit derivation dx

A: We will find the derivative.

Q: Compute / sin x •cos1º x dx.

A:

Q: Determine (tanx sec' x dx

A: We will evaluate the integral.     We know  sec2x - tan2 x = 1            implie, sec2x = 1+ tan2 x

Q: Find the value of

A: To find the value of ddxtanxx=π3.

Q: sin t cos t dt

A:

Q: Find dy/dx

A: y=∫tan x0dt1+t2

Q: | cos (nt)sin(at) dt Find

A: This integral can be solved by the method of substitution.

Q: |7t tan (1) dt

A:

Q: Derive a formula for tan x sec" x dxr where n# 0.

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: / (un"s tanʼ z + 1)* sec? a da tan? x +

A:

Q: Use Trigonometric Substitution to evaluate |x'V1-x° dx

A: put x= sin t for trigonometric substitution.

Q: Differentiate  (sin 2t)/t.

A: ft=sin2tt

Q: Differentiate the function. sin e + y = 4

A:

Q: find dy y = tan-1(ex2)

A: The given equation is y=tan-1ex2. To find the value of dydx. Solution: y=tan-1ex2 differentiate with…

Q: (B) Evaluate | tan (5x +1) sec³(5x +1) dx

A:

Q: dx is equal to 1+cos x O - cotx + cscx +c O - tanx + cscx + c O - cotx + secx + c O cotx + cscx + c

A: We have to find the integration and also find the limit in the second question.

Q: AN tan sec()dv A 2 2 2 14s 1YS

A: The given integral is,

Q: Evaluate tan x (t² cos 4t-3) dt dx Jo

A:

Q: Evaluate I = tan x sec x dx

A:

Q: What is ∫ tan x dx?

A: Integration

Q: Evaluate sin (x) cos(r)dx using an appropriate substitution.

A: Given that, I=∫absin5(x) cos(x) dx We have to find the solution of above integration.

Q: differentiate g(x)=sinx cosx tanx

A:

Q: Find dy/dx by implicit derivation. If tan-1(x2y) = x + xy2.

A:

Q: Evaluate sin (x) cos“(x) dx.

A: ∫ππsin6x cos4x dx

Q: Calculate tan x ( sec“ x ) dx using u-substitution with: (i) u = tan x (ii) u = sec x

A: I have stated the used formulas in the solution.

Q: please differentiate the function provided in the images

A: Given that

Q: Differentiate the function. y= (Sin x)In x

A: Given function - y = sinxlnx                   .............(1)Taking logarithm ln on both sides -…