Consider the following. P(q) = 3q2 +q + 8 (a) Find the derivative, by using the definition. p'(q) = (b) Find the Instantaneous rate of change of the function at any value. = (b), d Find the instantaneous rate of change of the function at the value q 9. p (9) = (c) Find the slope of the tangent at the value q = 9.

Q: Find the derivative of y = 6e x – cosx.

A: Given function, y=6ex-cosx Used formulas, ddxcfx=cddxfx  c=constantddxex=exddxcosx=-sinx

Q: 1. Find derivative of given function defined as follows. y = (8x²-3x³) ³

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Q: How to solve for the derivative of Dy[tan(y)+1/tan(y)-1]? If it's 0, why?

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Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

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Q: calculate the derivative with respect to x. ln(x2 + y2) = x + 4

A: Given function lnx2+y2=x+4 Differentiate the above function w.r.t 'x' ddxlnx2+y2=ddxx+4…

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

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Q: y = In- e 2x+1

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Q: What can we use to find the derivative of a function when it is impossible or difficult to isolate y…

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Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: 5. By calculating a derivative, determine whether the following statement is true (or false): et et…

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

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Q: Find the derivative of y=sinh-17x

A: Given:y=sinh-17xHyperbolic Identity:cosh2x-sinh2x=1Differntiation formula:ddxsinx=cosx

Q: Find a function y=f(x) whose second derivative is y''=12x-2 at each point (x,y) on its graph y=-x+5…

A: The second derivative of the function, y and tangent to the graph of y is given as,

Q: Find the derivative of the function. y = 2 cos5 x

A: Given, y = 2 cos5 x To evaluate, dydx

Q: 40 60 100 What is the derivative of y(t)?

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Q: 8. Find the derivative of the function. y= In(1+x)

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Q: Evaluate the derivative of y =e* sinh (2x). -3x

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Q: find the derivative of y with respect to the givenindependent variable. y = 2(s2)

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Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: 1 Find the function whose derivative is (x+1)-

A:

Q: Determine the derivative of the given function by using two different methods 2- 3) y = ² + 3

A: Given: y=x2-3x2+34

Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: Find the derivative Of U-5

A: Derivative of integration

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information.

Q: 1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

A: To find the derivatives of the given functions.

Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

A:

Q: Find the derivative of the function given by the equation y2=2px, where p is a parameter.

A: Given equation is Where p is a parameter. This equation is the canonical equation of  a parabola.…

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: Find the derivative of the function. h(e)- (-1) ( 1) +]

A: Given ht=t4-15t3+16

Q: Find the derivative of the function y = cosh−1(3x)

A:

Q: Determine the derivative of the following curve: T3+y3 +yi = 5

A: Given: x23+y23=5

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

A:

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: If fox) is odd function , then the derivative of y =coshf(-x)) equals

A: here option B is true

Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

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Q: Find the derivative of the function. simply if possible y = arccos(e2x)

A: We have to find the derivative of the function: y=cos-1e2x We know the formula of derivatives,…

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: How do I find the derivative of this problem?

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Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: Find

A:

Q: find the derivative of y with respect to the givenindependent variable. y = 2x

A: y=2x

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: How do I find the derivative of this problem?

A: