Examples : find the slope of the function's graph at the givenpoint. (use the definition of derivative) Or : find the slope of the curve at the point indicated. (use the definition of derivative) 1. y = vx+ 1 (x=1)

Q: f(x) = x2 - 3x + 5; x = 3/2, x = 2. Solve, a. Find the derivative of f at x. That is, find f′(x). b.…

A: Given function f(x)=x2-3x+5 and x=32,   x=2 To find: (a) f'(x) (b) the slope of the tangent line

Q: Dircc tion: Find the derivative of the following function: y= X1og10x %3D

A: Given function is  y = xlog10x

Q: Find the derivative of the function using the definition of derivative. 1 g(x) %3D 3 + Vx 1 (3+ vx…

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Q: っX+1\2 g(x) = x+1,

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Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = (3x − 1)−2 f '(x) =

A: Given the function is f(x) = (3x-1)-2, we have to calculate the derivative of this function.

Q: Match the graph of each function in (a)–(d) with the graph of its derivative in I-IV. Give reasons…

A: (a) Observe from the graph that the tangents are horizontal at two points. That means f'(x) has two…

Q: f(x) = x3 + 2; x = -1, x = 1.Solve,a. Find the derivative of f at x. That is, find f′(x).b. Find the…

A: To find the derivative f(x) differentiate f(x) with respect to x using the power rule…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). f(x) = x3…

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Q: Find the derivative of the function at the given point. (a)  Approximate the definition of the…

A: We have given a function :  f(x)=x1x  First we have to find the derivative of the function at the…

Q: x- 1. a. Find the derivative of y =

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Q: Find the slope of the graph of the function at the given point. Re) = t=3; G8) Use the derivative…

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Q: Find the derivative of the function using the definition of derivative. 1- 3t G(t) 4 +t G'(t) =…

A: In the function it is asked to calculate the derivate of function given G(t)=1-3t4+t.  Also it is…

Q: a. Find the derivative function f' for the following function f. b. Find an equation of the line…

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Q: a f(x) = x² sec (ax)

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Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = 1/3x-1   f '(x) =

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Q: Find the derivative of the function using the definition of derivative. G(t) = 1- 6t 4 +t G'(t) =…

A: Derivative of a function basically represents rate of change of the function with respect to a frame…

Q: Find the derivative of the function using the definition of derivative. 1 - 6t G(t) 4 + t G'(t) =…

A: We have G(t)=1−6tt+4Differentiating both side w.r.t "t" using quotient rule QUOTIENT…

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A: we have given the graph of the function f, it has local minima at x=2 (as it has minimum value in…

Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to…

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Q: Using the definition of derivative, find the derivative of f(x)=x^2+3

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: 28. F(v) V v+2

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to…

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Q: 2) Write derivatives (slope functions) for these functions y%=f(x); by hand, no calculator or Google…

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Q: Find the derivative of the function using the definition of derivative. f(x) = px + d f'(x) = State…

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Q: f(x) = x3 -2; x = -1, x = 1. Solve, a. Find the derivative of f at x. That is, find f′(x). b. Find…

A: the given function is fx=x3-2; x=-1, x=1 (a) we have to find the derivative of f at x that is value…

Q: Find the derivative of the function using the definition of derivative. u + 1 g(u) : 6u – 1 g'(u) =…

A: Given g(u)=(u+1)/(6u-1) now we will find g'(u) and domain of g(u) and g'(u) as shown below

Q: f(x) = x3 - 2; x = -1, x = 1.Solve,a. Find the derivative of f at x. That is, find f′(x).b. Find the…

A: It is given that;  f(x)=x3-2 differentiate with respect to x

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: 1. Using the definition of derivative, find the derivative of the follow Homework: 1. Using the…

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Q: Find the derivative of the function g(x) 4 – 2x g'(x)

A: We have to find the derivative of the function g(x)

Q: The graph of the derivative of a function is given. Sketch the graphs of two functions that have the…

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Q: Calculate the derivative of the function. HINT [See Example 1.] g(x) = (2x2 + x + 4)−3 g'(x) =

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Q: Calculate the derivative of the function. HINT [See Example 1.] f(x) = (x – 4)-1 f'(x) =

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Q: The graph of the derivative of a function is given. Sketch the graphs of two functions that have the…

A: From the given graph, it is observed that the derivative of the function constant and its constant…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: 2 5. f(x) = x3

A: We will use the definition of a derivative to solve this question.

Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given: a = 11…

Q: Find the derivative of the function using the definition of a derivative. State the domain of the…

A: The derivative of g(t) with respect to t is defined as

Q: Using the definition of the slope of a tangent line, find the derivative of each function. 1. f(x) =…

A: Given:- 1) f(x) = 2x - 6 2) g(x) = x2 + x - 1 3) h(x) = √(4x)  To find:- Slope of tangent line by…

Q: The graph of a function is shown together with the tangent line at a point P. y 7. 6 P. 5 4 3.

A: The slope of the tangent line at a point on a function is equal to the derivative of the function at…

Q: Burma: user what is the definition of a derivative very derivative of the function y = 1/3

A: Topic:- calculus

Q: a. Find the derivative function f for the function f. b. Find an equation of the line tangent to the…

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Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to…

A: For (a), We need to find the derivative function f' for the function f(x)=2x2-9x+10. So,…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Using the definition of derivative, find the derivative of the following functions: (a) y=F-2 (b) y=…

A: d(xn)dx=nxn-1 is basic formula