( al=) if x # 0 1ifx 0 6. Let f(x) = borln Find f'(0).

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y * logy x *

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Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: If z = +3y, find the differential dz. dz =

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Q: Is the derivative of Jx* sin (1/x), x 0 h(x) 1o. x = 0 continuous at x = 0? How about the derivative…

A: Answer(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…

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Q: Which of the following means "first derivative" * O f(x) O y' O dy/dx all of the above

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Q: dy by implicit differentiation if dx 3 9. = 1. Find - -

A: The given function is 3y+9x=1

Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

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Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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

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

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A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: s+a Using differential and integration of transforms, find f(t) if L[f] equals In s-a

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Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: Find the differential d3y of the function y=xsinhx.

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Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: 5) y>10 (3v-1) (1+5w)

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

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Q: - Using the integral definition of gamma function show that T(7) = 61(6)

A: Integral definition of gamma function is Tx=∫0∞tx-1e-tdt . Put x=7 in Tx=∫0∞tx-1e-tdx and simplify…

Q: Evaluate the second derivative of e22.1.png а f(x) acos(b/x) x2 if a = 345 and b = 0.6 at x = 5…

A: Given: Let us consider the given, fx=acosbxx2 where a=345 & b=0.6 at x=5 using BDA with ∆x=0.06.…

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: Find values of p for which integral diverges. dx x(In x)"

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

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Q: What is the derivative of this integral?

A: We know that

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y * logy x |

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Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

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

A: To differentiate

Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: Eliminate the arbitrary constants x = -ln t , y = at + bt^2

A: given  x=-ln t , y=at+bt2 claim- to eliminate the arbitrary constants

Q: 19 f(2) = | t² dt then f'(x) = If Find the derivative of g(x) = sin(t') dt. g'(x) =

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Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

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Q: . Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0. f (x) has a root in [0]. If we…

A: Newton-Raphson iteration scheme is given by  xn+1=xn-f(xn)f'(xn) We use this formula to estimate…

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

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Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

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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…

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Q: Evaluate S 0 2-9.x² dx using the Gamma function.

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Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

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Q: 6 The coefficient of sin( 2r) in the antiderivative of F(x): F(x) = (cos( is

A: We have to find the coefficient of sin 2x.