10+ -10 10 -5- f and g are fonctions and f(gcx) 9cx)= f(x)/gcxs hcx) = How can and qico) 主 find h'(-3)

Q: (1) Sinx-26 2. (20) f(x)%=Sinx-Gx

A: (19) fx=sin2x−2cos2xsin2x−2cos2x≥02sinxcosx−2cos2x≥02cosxsinx−cosx≥0Case 1:2cosx=0 and…

Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

A:

Q: (a) Find the equation of the tangent line to the graph of the function f(x) = 3x² at the point (-2,…

A: (a)   Differentiate the function with respect to x is,   Substitute -2 for x in the above equation.

Q: f(x)=(x^3-25x)/(7x^2+1) Use the first derivative test to find the critical points.

A: Given: The function, fx=x3-25x7x2+1.

Q: 16. etan (1) sec² (x) dr

A:

Q: Find the first and second derivative of (x^3-3x^2+5)/(x^3+1). I found the first derivative, I…

A:

Q: rin 2 e2# sec-"(e")dr

A: Solution

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

A:

Q: Use second derivative test, If f(x) = 4x +9 then f(x) has a local maximum at the point 3. I= 3 I =…

A:

Q: 9-2a æ f (x) = 5xe®- Find the Critical Points Find where the first derivative is equal to 0. Enter…

A:

Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: 1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and…

A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

Q: sin (2x) cos (2x) csc (x) 2. Determine the limit of · xVx4 as x approaches 0

A:

Q: əz az 6. Use implicit differentiation to find · ax and if z is defined implicitly as a function of x…

A: We will differentiate partially both side of the equation with respect to x and y.

Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A:

Q: .4 -1 sec J2 Evaluate x dx

A:

Q: Use second derivative test, If f(x) 4x +4 then f(z) has a local maximum at the point %3D I = -3 T= 3…

A: This question is based on maxima and minima of function.

Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

A:

Q: Use the second derivative to discuss concavity. The second derivative is y’’ ={2x(x2+3)}/ (x2-1)3

A: given,  y''=2xx2+3x2-13 we have to discuss the concavity using second derivative.

Q: 1) Find All solutions For y = 3.0 to the Transcendental equation: sinx-ln z = X - Y + gamma x This…

A: note : we will refer the term "gamma" at the end of the  equation as the symbolical constant : γ =…

Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 6] y= 4x+2–- 5x6 Standard Form: Degree: Sign of LC: as x→-0, y → as x 0, y→

A:

Q: 6. Use implicit differentiation to find first order partial derivatives: tan-(x²y) = y²z3 +…

A:

Q: Find the equation f(x)=1+csc(x)-√ cos(x) at the point (2π/3,4+ √ 3/2 √ 3

A:

Q: 6/5 (3 - x). x5/6 The derivative of the function y = In is y' = %3D

A: we have to find derivative

Q: 2x-5 4. f(x) = x2+4x-5 sin x 5. f(x) = cos x

A:

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

A:

Q: 10 If f (x) dx -7 and f (x) dx = 1 then determine -3 -3 10 [1- f(2) dz 5 showing working.

A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

Q: =x+6 Line 1: y= 2 Line 2: y=x-1 =-x LI

A: In system A, L1:y=x+6L2:y=-x The graph of the lines are intersect at one point. Hence there is…

Q: f(x) = -12sin(x)cos(x) f’(x) = -12cos(2x) f’(π/6) =

A:

Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

A:

Q: 7) f(x) = sin² x+ cos² x %3D Cosx-Sin X Sin X Sinx t cosx

A: Given

Q: - Find All solutions. For y = 3.0 to the Transcendental equation. sinx-ln z = X - Y + gamma x & This…

A: note : the last term in the given transcendental equation is "gamma" which is used to represent the…

Q: Verify that f has inverse function then use function f and the given real number a=2 to find…

A: Given information:

Q: QI/Solve by mean value theorem 1- F(x)=x² In the interval [1,-1] 2-F(x)=coshx In the interval [-1,3]…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find an anti-derivative for each function in C equals zero

A:

Q: Proove: Yn- n-1 x

A: Given That : Let us assume that  y=xnlog(x) Prove that : yn=n!x using Leibnitz  theorem

Q: / Vtan(x) d.x sin(2r) I Vtan(x) -dx sin(2x) -d.x sin x cos x /cos x 2 Multiply by something that is…

A: We have to find integration

Q: 1. f(x) = cos 3x2. y = - tan 12x3. f(x) = sec x? 4. y = sin(2x² + 5)5. y = 12 csc6. f(x) = sin(x +…

A:

Q: Use second derivative test, If f(x) = 4x+4 then f(1) has a local maximum at the point I = -3 I = -2…

A:

Q: Suppose f(x) = 2ax3 + b3x − 4c where a, b and c are real constants. Suppose that f has a horizontal…

A: f(x) = 2ax3 + b3x - 4c    Differentiating wrt x,    f'(x)  =  6ax2 + b3

Q: 11) у %3D 14-X Find the derivative. ex 8) у %3D In x

A: topic - derivatives

Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x<0x         0<x<2-x2+4x-2…

Q: 3 8. y = sec Зx) 9sec (2 – 3x)tan´(2 – 3x) B. - 9sec (2 - 3x) tan tan (2 3 С. 9 sec' (2 — 3х) tan…

A:

Q: x² - 5 X-3 -, x#3. Then use the second-derivative test on each critical number to determine whether…

A:

Q: 1. State the power rule. 2. For which values of n have we proved the power rule? 3. Based on your…

A: 1. The power rule of derivatives gives the following: For any real number n,      ddxxn=nxn-1

Q: 6. Find all relative extrema of the function h(x) = -3x5 + 5x3 using the Second Derivative Test.…

A: Relative maxima and minima

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: