Express y as a function of x. The constant C is a positive number. ln y = ln x + ln(x + 1) + ln C

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x c. f(x)= x²e* – 6x

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Q: 1. Find the slope of the line tangent to the function f(x) = 7 ln(x) – 6x at the point (1, -6). %3D…

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Q: 1. Find the function whose derivative is XV X xª – 1

A: We need to find a function whose derivative is 1xx4-1

Q: 6. Find the derivative for each function, and simplify (reasonably): a) j(x) = (3x² + 3x – 1)* b)…

A: According to the chain rule of differentiation:   According to the Product rule of differentiation:

Q: Fnd the derivative of the following functions. 6. f(x) = (2x3 - 3)(x2 - 4x) 5x-3 7. h(x) = 8. g(x) =…

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Q: Find the third derivative of the given function g(t) = Square Root of 5t+3

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Q: (A) Find the derivative of t² – 1 y = t2 + 1

A: The identity used is d(uv)dt=v *dudt-u*dvdtv2 where, u and v are the functions of t.

Q: Find the first and second derivatives of the function. g(t) = t°(6t + 5)* g'(t) g"(t) =

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Q: 2. Find the intervals of increase or decrease. a) ƒ(x)=x ln x b) f(x) = xe* c) f(x) = xe¯* d) ƒ(x) =…

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Q: 1 1 In?x Find the function whose derivative is Inx 1 A x2 1 B xlnx C) xlnx D Inx 1/x

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Q: The derivative of the function - is equal to e Select one: a. a(2º In 2 + 1) b. e" (2ª In 2) c. e"…

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Q: 6. Find the derivatives of each function. a)f(x) = 3x4 – 4x² – 250 %3D b) g(x) = x/2 – x-1/2 %3D sin…

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Q: 12. Find the derivative of each function. 4x (a) f(x) = 2x2 -1 f (x) = (2x – 1)²(3x + 2)3 f (x) =…

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Q: Зх-1 -dx 2 x+1

A: Given query is to find the integral.

Q: Find the requested value of the second derivative of the function. 3 f(x) = x* + 4x° - 4x + 4; Find…

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Q: -e' 4. Y = e3x +e¬3X

A: Given: y=e3x-e-3xe3x+e-3x

Q: The derivative of the function is equal to Select one: O a.e (2* In 2) b. e* (2* In 2 + 1) c. x(2*…

A: Given function is By using the law of exponents x^m/x^n=x^(m-n), we get Differentiating with…

Q: Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*)…

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Q: Calculate the Implicit Second Derivative for the function shown  1) b(z)=(z-5)^2 2) Find the value…

A: The function is given by bz = z-52 To evaluate: 1) The second derivative b''z          2) The value…

Q: The function is given by implicitly by the equation xy² +x?y+x?y² = 3. Find the derivative of y in x…

A: Here we use derivation in the function

Q: Find f’(e) of the following function. f(x)= x3 *(ln x- 1/3)

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Q: 4. Find the derivative of each of the following functions. (a) f(x) = (x? – Va) - e* (b) g(x) c+ re

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Q: Find the third derivative of the given function. o1) = ()2 - 3)* g"(t) =

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Q: Find the first and second derivatives of the given function. f(x) = e *(3 + 3x)? Calculate f'(x).…

A: The given function is fx=ex3+3x2

Q: 1. Find the natural domain and the derivative of the given function. (a) 3x² +7x + 5, (b) (3x +1)5,…

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Q: Find the second derivative (y") of the following function step-by-step and simplify the final…

A: y=e-3x+4+2e2+3x+1 take the first derivative y'=ddxe-3x+4+2e2+3x+1…

Q: Find all the higher derivatives of the function f(x) = (4x-5)°. P (x) =] f"(x) = f"(x)=

A: Differentiate above function with respect to x

Q: Find the first derivative of y with respect to x (y') of the given function. y = ((U^2 - 1) / (U^2…

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Q: 2. Find the derivative of each function a) y=(2x+5)/(3x-2) b)f(s)=((square root of s)-1)/((square…

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Q: Calculus tells us that we can find the locations of the extrema of a function g(x) by calculating…

A: We need to find the iteration formula for Newton Raphson method to find the extrema of g(x) we know…

Q: Find the derivative of the function. g(x) = e2a-5z+3 (6x? - 5) e2³–5x+3 O 23-5x+3 e622 -5 (2x - 5x…

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Q: Find the value or values of c that satisfy the equation f '(c)=f(b)-f(a)/b-a in the given interval…

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Q: 38. Determine the derivative of each function. b) g(x)=5 -10* d) f(x) = xe* a) y=-2e* ) h(x) =…

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Q: (A) Find the derivative of t2 – 1 y = t2 +1

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the natural domain and the derivative of the given function. (a) ln(4x + 2) (b) x · cos x (c)…

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Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

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Q: A function f(x) is defined by f(x) ce Find the value of the constant e for (x) dx=1.

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Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

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Q: x°y- xy? +x² + y² = 0 %3D

A: Use d(UV) = VdU+ UdV

Q: Q8: Find the second derivative of the function: f(x) = x² + e* + 1 %3D Select one: f"(x) = 3 + e* a.…

A: The derivative of the function can be calculated by differentiating the function with respect to a…

Q: Find the second derivative of the function. f(t) = t?e-5t f"(t)

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 24x, f'(1) = 0, ƒ(1) = 20 %3D

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Q: 4. k(x) = (4x³ – 7x² + 5)/4e*

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Q: d for the function dx f(x) = (8x – 5) (3æ² + 7)* Find using Logarithmic Differentiation

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Q: Find the first and second derivatives of the given function. f(x) = e ×(1 + 4x)2 Calculate f'(x).…

A: Given: fx=ex1+4x2

Q: Let a and n be positive integers such that a < n. If the derivative of the function y = ar" + næª is…

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Q: 6. Find the second derivative of the function. f(P) = v1– 2P7 eC-2P

A: Some derivative formulas: ddx(fg)=fg'+gf'ddxfg=gf'-g'fg2ddx(a)=0ddx(xn)=nxn-1

Q: Find the first derivative of exte-2 y = = ܘ ܘ e+ܫܐܕ 2k+e ye+e 2 ܪܢܐ e+e 2 ܢܐܨ ܐ e+e

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Q: 2. f(x) = 2x – 5x%

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.