Let fx) e sinx. Calculate and simplify f "(r)

Q: Compute the following derivative: tan e dr 30 – cos 0

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: let f(x)= cos(x)-sin(x)/ h(x)ex, what is f'(x)?

A: Find f'(x) fit given f(x)

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Integrate the following. - sec²x 3. ( sec?x tanx

A:

Q: Express cos°x as a function of multiple angles.

A: The function of multiple angles is given below,

Q: Integrate sin" uelog(cosu) . Where n=666

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: Evaluate fe'(si Je*(sin x +cos x)dx

A:

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: If f(x) = 5x(sin x + cos x), what is f'(x)?

A:

Q: Find f' (x), if f(x) = sin(2x* – sin(x))

A:

Q: Evaluate Je sin(3x) dx

A:

Q: Li sin sin dx = where m n 04: Prove that: %3D where m = n

A: Topic:- integration

Q: - f(t) = teat sin bt

A:

Q: Write 6 sinh(x) + 3 cosh(x) in terms of ex and e−x.

A: here given that 6 sinh(x) + 3 cosh(x) the value of sinh(x) and cosh(x) are.. sinh(x) = ex/2 - e−x/2…

Q: If f(x) = => (1- (sinx)?)" .Determine the value of f( %3D n=1

A: by using geometric progression

Q: Can the Fundamental Theorem of Calculus be used to find 5xcosx?dx?

A: This question can be solved by applying the second part of fundamental theorem of calculus.

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: 3. f sin√tdt

A:

Q: Integrate sin" uelor (cosu) . Where n=540

A:

Q: Consider the function f(x) whose second derivative is f"(x) = 7x + 10 sin(x). If f(0) f(x)? 3 and…

A:

Q: Let 5 sin x + 6 cos y = 6. dy dx d²y dx?

A: Given that 5 sin (x)+6 cos (y)=6 -(a)Our Aim is to find  (i) dydx and (ii) d2ydx2

Q: 10) )Eind fCx) if f Gx)= arc sin Se 0.00

A:

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

A:

Q: If a>0 is a constant then sec (ax) tan (ax) dxD

A: Assume sec(ax) = t,

Q: Evaluate: cot[ sin! V212] O 2. O VZ 12

A:

Q: tim Sin It tanx\

A: We will find this limit by substitution

Q: Find anti deriva tive Fa) of the function, an foal- fxl = 5 sinx such that Flo) = 8+ cosX

A: Now,

Q: Evaluate fx sin(x)² cos(x) dx.

A:

Q: If Y= Sečx + tanx ,fnd dy when X=0 ? 3 IF Y Secx +

A: Given that y = sec3x + tanx . Find (dy/dx) use x = 0. Here i attached full solution of this question…

Q: Simplify tan(t)cot(t) to a single trig function or constant with no fraction

A: To Simplify tan(t)cot(t) to a single trig function or constant with no fraction

Q: If f(x) = [sin(x)]², what is f'(x)?

A:

Q: Evaluate f S sin tdt

A: We will evaluate the integral as following.

Q: Differentiate the function.

A: Given

Q: Express the following as an algebraic function of x. sin(arctan(2x) + arccos(2x))

A: Question is solved.

Q: Write the definitions of the hyperbolic functions , sinh  x  ,cosh x , tanhx

A: Solution:- Definition of the hyperbolic functions, a) sinh x b) cosh x c) tanh x

Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

A: Given that, fx=x5arcsinx27To find f'(x)

Q: If f(x) = 3 sin(4æ) arcsin(x), find f' (x).

A:

Q: Find the tangent of 2X. Х. 13 Y 12 Write your answer as an integer or as a decimal tan (X) %3D 5.

A: this is the right triangle

Q: Hiw / By using inverse function f ind: Sin(zti)=4i

A: To find: sinz+i =4i using inverse function

Q: Calculate f'(1), where f(x) = arcsin(x 2)

A: given, fx=arcsin2x now differentiate given function f'x=21-4x2

Q: If f(x) = cos(sin(x°)), then f'(x)

A: The givne function is f(x)=cossinx6 We have to find f'(x)=?

Q: 1. Differentiate each function by using formulas. t cost (b) у %3D COSX (a) f(x) = 1+sinx

A:

Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

A:

Q: Let y = sinx, if y(n) = sin x then n =

A: This question can be solved using the concept of higher order derivatives.

Q: (a) Use S(f) to estimate |sin e" dr.

A:

Q: Evaluate ∫ex cos3(ex) dx using tables after performing the substitution u = ex.

A: We have to evaluate the integral by substitution method: ∫ex cos3ex dx Substituting, u=ex…