For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0 (f(x+h)-f(x))/h f’(x)= ?

Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

Q: Find derivative of 2x^4y^3-xy^2 using chain rule.

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Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

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Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: f(x) = (6x² - 2x+1)^

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Q: Find the general solution using reduction of order. 1. y''=ln(x)

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Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

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Q: show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

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Q: 10. f(x) = cos (2x)e*²-1

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Q: How to find the critical points of this derivative

A: We have to find critical point of f(x),where f'(x) is given by:

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: fx て (X)

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

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Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

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Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Find the derivative: y = ln(24) 2x-4 O 4x-x² 2x-4 x²-4x 4 4x-x² 4 x²-4x O о O 8

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Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Use the sign of the derivative to establish the inequaltiy ln(1 + x) > x − x2 2 , ∀x >0

A: SOLUTION-

Q: Find the derivative of the function by the limit process.

A: Given: fx=x3-12x

Q: How do you find the derivative of f(x) = 5 using the limit definition of derivatives? I know it is…

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Q: Find the derivative of the function by the limit process. f(x) = 7x − 3

A: GIven function: f(x) = 7x − 3 Formula used:

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

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Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: Find the partial derivative. 4 = (x² + 6x – 3y)* - dz

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Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

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Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

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Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Find the derivative using the long method 3-t to

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

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Q: Find the relative extremum of g(x) = x - 3x +1 by using first derivative test.

A: Let g(x)= x3-3x2+1 To find the relative extremum , here we use first derivative test In this method…

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is…

A: The derivative is given as

Q: 2. Find the derivative In (x+) y3=

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Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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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: