If f/g(t)dt = sin(x) for every x, find g(2 x). g(2 x) =

Q: Find the differential d4y of the function y=x5.

A:

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

A:

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: Compute the derivative d/dx of the following functions: y = 2 sec x − csc x x cos^2(4x)…

A: y = 2 sec x − csc xDifferentiate w.r.t.xdydx=ddx( 2 sec x − csc…

Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: Find the derivative of the given function. 5x y= In 6+x dy dx

A:

Q: Find dx/dt: x = 2[cos (t/2)]^2

A: x=2cost22

Q: d Use the Fundamental Theorem of Calculus to find the derivative. dx dt 1+ vE

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

A:

Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Find the differential of the function. u = 2x +

A:

Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: In (6x) Find the derivative of y with respect to x if y = sin (3e) dt.

A: the given function is: y=∫0ln(6x)sin3et dt we have to find the derivative of y with respect to x.…

Q: If z = (x + y) e and x = 6t and y = 1 – t, find the following derivative using the chain rule. Enter…

A: In this question we have to find the differentiation of z with respect to t.

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

A:

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Find the differential d3y of the function y=1/√x.

A:

Q: Find the differential of the given function y = xcosx

A: To differentiate

Q: If 3xy+x^2=7 and dy/dt=-16, find dx/dt when x=1

A: Derivative, in mathematics the rate of change of a function with respect to a variable. Derivatives…

Q: Calculate the derivative e8x d In (t)dt dæ using Part 2 of the Fundamental Theorem of Calculus.…

A: Given To apply the fundamental theorem of calculus first simplify these integrals so that this…

Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

A:

Q: Find the differential of the function. = e dy =

A: y= e^(2x) dy = 2 e^(2x) dx

Q: Suppose g(x) = = A, and f' (1) = B. Find the derivative In(In(In(f(x)))), %3D f(1) = dg dx \x=1…

A:

Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

A:

Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3

A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…

Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

A:

Q: Find the derivative of the following function. y= In (In (4x)) dy dx

A:

Q: 3 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

A:

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: 1. F(x) = S, t³ - 5t dt

A:

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

A:

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

A:

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

A:

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,