Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) -1 1

Q: Find the derivative of the function. 3x 9(x) = e+5.

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Q: Find an equation of the tangent line to the graph of the function at the given point,

A: To find the slope we find y' at x=2 and y=1 so the slope is 2

Q: Find the equation of the tangent line to the function f(x) = e*-1 In(x + 1) when x = 0.

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Q: y = 7x + e5x ; (0, 1) %3D

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Q: Find the derivative of the function.

A: We know that, logbx=y if and only if, x=by. Also, logbxn=nlogx

Q: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

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Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e*…

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Q: Find the differential of the given function.

A: Given function - z = 1-2v+v4-23Differentiating on both sides with respect to v -dzdv =…

Q: Find the equation of the tangent and normal line of the function y³ + 3xy + x* = 5 at the point (1,…

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Q: Find the derivative of the function. y = In(e7x + 5)

A: Given y=ln(e7x+5)

Q: Find an equation of the tangent line to the graph of the function at the given point. y = ln(x7/2);…

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Q: Find the equation of the tangent line to the graph of function at the given point y = 1n x^4 ; (1,0)

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 – x? –…

A: Given:    y=4-x2-ln12x+1 at (0,4)   We are given that x0=0   The value of function at given point…

Q: Find the derivative of the logarithmic function. 6 + y = In

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Q: Find an equation of the tangent line to the graph of the function at the given point f(x) = e−x ln…

A: we have to find the equation of the tangent line of the given function at the point (1,0)…

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

A: Our Aim is to find an equation of the tangent line to the graph of the function f(x)=e-x-6-(i) at…

Q: Find the derivative of the function.

A: Given: f(x)=log2x2x-1

Q: Find the derivative of the function

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Q: Find the slope of the tangent line to the graph of the function at the given po y = e 5x y (0, 1) -2…

A: Given curve y=e-5x, point 0,1. Differentiation with respect to x we get…

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

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: The slope of the tangent line x = e*, y = In e3x

A: Let's find.

Q: Find an equation of the tangent line to the graph of the function y = log10 2x, at the given point…

A: Given:y=log10 2x  through the given point 5, 1Equation of tangent line:y-y1=mx-x1Slope:dydx=f'x=m

Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

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

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Q: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

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

A: We have given function  fx=e-xlnx Then, f'x=-e-xlnx+e-x1x=-e-xlnx+e-xx Therefore,…

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e=*…

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Q: y = log,(4x - 8x)

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Q: Find the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

Q: Calculate the derivative of the following function. y=2 log5 (x -3) 2 log5 (x-3) = (²-3) =] dx

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Q: Find an equation of the tangent line to the graph of the function                   y=2x2 + ln x2 ,…

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Q: Find an equation of the tangent line to the graph of the function at the given point. g(x) = ex3 −…

A: We have been given a function g(x) and we need to find the equation of tangent line to the graph of…

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: Find an equation of the tangent line to the graph of the function f(x) = e6x, at the given point (0,…

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Q: Find the derivative of the function y = log5 √(x2 − 1 )

A: Here given function as y=log5x2-1 or y=log x2-1log 5 The power rule for derivatives is expressed as…

Q: Find the derivative of the function. h(x) = log,(x + 9) h'(x) = %3!

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Q: find the equation of the Tangent and normal line of the function y3 +3xy + x4 =5 at the point (1,1).

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Q: Find an equation for the tangent line of e + 2xy = 2x – 1 at (1,0).

A: Topic- application of derivatives

Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

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Q: Find the derivative of the function

A: given h(x)=log3xx-12we have to find the derivative of the given function

Q: Find an equation of the tangent line to the curve at the point (1, 1/e)   y = x3e−x

A: Given query is to find the equation of tangent line to the curve   y = x3e-x

Q: Solve for the derivative of the following Exponential Differentiation. 1. y = 92x^2 + 3x +1 2. y =…

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = lnx4…

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Q: Find an equation of the tangent line to the graph of f(x) = 2 + e1−x at the point (1, 3).

A: We have to find equation of tangent line to the graph of function fx=2+e1-x at the point 1, 3. We…

Q: Find an equation of the tangent line to the graph of the function at the given point, y = e3x−x2,…

A: Given equation: y=e3x-x2 The equation of the tangent passing through the point x1,y1 on the curve…

Q: Find an equation of the tangent line to the graph of  y = e−x2  at the point (5, 1/e power of 25)

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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: