Use f'(x)= lim h-->0 f(x+h)-f(x)/h to find the derivative at x for the given function. s(x)=5x+8, s'(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: Find the derivative of the function using the definition of derivative. 1 g(x) 2 + Vx = (x), E State…

A: Given problem can be evaluated as follows:

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

A: Given :            y = 4(x + 2)2 , (0, 1) To find the slope of the function at the given point.

Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: 5y + xy-

A: Differentiation: 5y+xy-4=0 ddx(uv)=udvdx+vdudx ddx(y)=dydx

Q: valuate the second derivative of the function at the given point. Use a computer algebra system to…

A: The derivative of the square root function is calculated using the formula ddxxn=n·xn-1. The value…

Q: Using either limit definition of a derivative at a point, determine the equation of the tangent line…

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

A: Differentiate the function with respect to x using the chain rule to find f'(x). According to the…

Q: Find the derivative of the function. State the domain of the derivative. f(x) = [In(x)]6 f '(x) =…

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Q: ing the limit definition of derivative, find the third derivative of g, given g'(x) = 2-√√x+1

A: Note that, according to Bartleby Guidelines, In the case of multiple questions, we can answer only…

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: 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 equation f(x)= x^2+x find slope of tangent line f′(2) using the limit definition of a…

A: The slope of the tangent is given by f'(x). We will use the limit formula to find f'(x)…

Q: 4. Find the derivative of the function using the definition of derivative. State the domain of the…

A: f'(x) = limh→0 f(x+h)-f(x)h. The domain of the function is the set of all possible input values for…

Q: Using the limit definition of derivative, compute the derivative of the following function. No…

A: by limit definition of derivativesf'(x) =limn→0 f(x+h)-f(x)hf(x) = 3x2-2xf(x+h) = 3(x+h)2- 2(x+h)

Q: Give an example of a function that is continuous on −∞ < x < ∞, but has NO DERIVATIVE at x = 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…

A: The function is F(x)= 2/x2 And the point is (1, 2)

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

A: Given: f(x)=5 x3-2-1 To determine: Slope of the given function at point -2, -12

Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

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Q: 2. how does differentiability and continuity determine the derivative of functions?

A: Differentiability and Continuity

Q: using the derivative definition how do I find f(x) = -6(square root over x).

A: The limit definition is on the board . First we find f(x+h) amd substitute the value in the limit…

Q: Find the intervals of concavity and points of inflection of y = x+In(x² + 1). Make sure to show all…

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Q: Using the derivative of 10x determine the value of the derivative at   x=3 and x=5

A: Derivative ( xn) = n xn-1

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

A: The slope of tangent to a curve y=fx  at point a,b is given by dydxx=a.

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: Given function is fx=1x+4. Compute the first derivative. f'x=1x+4'=-12x+432

Q: What is the derivative of f (x) = 3x³+2x using the limit definition (please use delta x if possible)

A: A detailed solution is given below

Q: Using Chain Rule method Find the derivative of: 5 2. F= x³ + x² + x + 1 1. F(x) = ln Cos(x²)

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Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 10 -2 4…

A: The given function is fx=-3xx+2.

Q: Il relative extrema of the function f(x) = x* - 4x2 +2 by using the Second Derivative here…

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Q: 5. Use methods of calculus (Derivative Tests, etc.) to find the relative extrema and inflection…

A: function has local minima at x=2 function has local maxima at x=-2 and x=0 is the point of…

Q: Find relative extrema not using the first derivative test   s(x)=x^4-2x^2

A: We will use the second derivative test. But the route to second derivative passes through the first…

Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: e Second Derivative Test to find all relative extrema of g(x) = x³ – 3x² +3. Show your work.

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Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Use the definition of the derivative to compute the derivative of the function f(x) = 1 – 6x² at an…

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Q: Find and classify the relative extrema of the function, if they exist. You MUST use the…

A: Given :fx=2xx2+1

Q: se the limit definition of the derivative to find the slope of the tangent line to the curve f ( x )…

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Q: Using terms like "secant line" and "tangent line", explain how evaluating f(3+ h) – f(3) lim gives…

A: This is a problem related to derivation of the general formula of differentiation.

Q: Using method of sub., find the Anti-derivative 1 x In x

A: detailed solution is given below

Q: Find the derivative of the transcendental function. y = 6e^x/(x^2+5)

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) = V3 + x f'(x) =…

A: We need to find derivative of the function fx=13+x and its domain

Q: Find the derivative of the function. y = arctan(root1-x/1+x)

A: y=arctan1-x1+x

Q: 4. When finding the derivative of a fraction you have to use the Quotient Rule. 5. The derivative of…

A: 4. when finding the derivative of a fraction you have to use the quotient rule.5. The derivative of…

Q: 5. Calculate the derivative of x* sin (x) showing all your work. 6. Use the limit definition of the…

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Q: 5. f(x) = 3-5x+ x use limit definition of derivative)

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Q: Find an equation of the tangent line to the graph of y = f ( x ) at the point on the graph where x…

A: The slope of the tangent line of a graph y = f(x) at a point x0 is given by the derivative of…

Q: Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).

A: The given function is: f(x)=(x)(1-2x)3 And, at point (1,-1), we have to find the equation of the…

Q: 3 sin(x) +x² In(x) – 2x Find the derivative of f(x) = using derivative rules.

A: