Suppose f(x)= √1 − 3x a. Use the definition of derivative to find the slope of the tangent line to the curve at x = −1. b. Find an equation of the tangent line to the curve at x = −1.

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

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Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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Q: Suppose f(x) = e**+5x+7. Find the df derivative dx f'(x) =

A: We have to find

Q: Find the derivative of the function.

A: Consider the provided function, ht=t2t3+22 Find the derivative of the function. Apply the chain rule…

Q: For the given function f(x), determine the equation of the tangent line at the point P(1,1) f(x) =…

A: Equation of tangent line

Q: Find the equation of the tangent line to the curve f(x)= x2 +5x when x=1.

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Q: Find the derivative of function defined as follows.

A: Given: fx=82x2+5 Differentiating the given function fx with respect to x, f'x=ddx82x2+5…

Q: 2x+4 f(x) = (3x + 7) e.

A: Given query is to find the derivative of f(x).

Q: Given the function y=x2cos3x. Find the third-order derivative.

A: To Determine: Third derivative of given function:

Q: Find the derivative and simplify A. y =((x2)/(2 + lnx)) B. f(x) = ln (√((4x + 1)/(5x + 7))

A: We have to find

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Q2. Find the slope of the tangent line to the function f(x)= at x 4 by using the 2Vx definition of…

A: Given that,

Q: Given f'(x) = 2x – 6 is the derivative of f(x) = x² – 6x + ß , find a if f(x) is to be…

A: Let's find.

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A:

Q: Find the derivative of f(x)=x^2 e^2.5x

A: Given problem:- Find the derivative of f(x)=x2 e2.5x

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). f(x) = x2…

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Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A: Given: Use the alternative form of the derivative to find the derivative at x = c, if it exists

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: For what values of x is the derivative of the function Vx2+ Vx equal to 1?

A: Given,           The derivative of x23+x3 equal to 1.

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Given the function z=(x2+1)(x−1). Find the value of its derivative at x=−1.

A: The given function is z=x2+1x-1

Q: Find the derivative of the function: f(x)= e^x÷x^2

A: Given,

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: Given y=3x-2x2. Find its derivative and show that when x=5, a small change in x by P% will cause y…

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Q: Find the derivative of function defined as follows.

A: Derivative of the function can be found with the help of differentiation of the function.…

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

A: Given: fx=x3+2x2+1 , c=-2 To determine: Derivative of given function at x=c

Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: Find the derivative of the function f(x) = 36x arccos(4x) + 9/1 – 16x? f'(x)

A: we will solve using product rule and chain rule of derivative

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A:

Q: For what values of x is the derivative of x equal to the derivative of x2 + x?

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Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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Q: Compute for the derivative of the function below for x = 1. f(x) = 2xe

A: Solution: dydxx=1=2xex

Q: Let f(x) = 3x^2 + x + 5. a) Find the equation of the tangent line at x = 10. b) For what value of x…

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Q: For ƒ(x) = ax, find ƒ″(x) and ƒ‴(x). What is the nth derivative of ƒ with respect to x?

A: Since, we have been given that f(x)=ax-(i).Our Aim is to find f"(x) and f'''(x).Also, we have to…

Q: if x=t^2+1 and y=t^3, then the second derivative is?

A: x=t^2+1⇒dx /dt​=2ty=t^3⇒dy/dt = 3t^2​

Q: Find the derivative of the followi (a) x = t2 + 5t + 4, y = 4t

A:

Q: Find the derivative of the linear fractional function y=ax+bcx+d.

A: We have to find the derivative of    y=ax+bcx+d ddxy=ddxax+bcx+dWe have to apply division rule…

Q: Find derivative of the 6tanx following function d d.x

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Q: Find the derivative of f(x)=(x−2)e^(−3x).

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

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

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with…

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

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Q: Solve by definition of derivative if f(x)=x+Vx AND also Find x? w.r.t x*

A: fx=x+x Now by the definition of derivative, we have…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = x2…

A: Solution:-  The given function is  g(x)=x2-xwe have to use alternative form of derivative to find…

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

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Q: f(x) = Vx + 9

A: We have to find the derivative of the function: fx=x+9 We know the formula of differentiation,…

Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: Find the exact equation of the tangent line to the curve f (x) = x³ + 3x +4 at x = 2.

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Q: By using the definition of the derivative, find d/dx   1/(2−x).

A: