A function is given as x - 6y = 5– x. Calculate the derivative of y with respect to r with two different methods:

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

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Q: Find derivative of the following function. 5x -5x y%3D dy

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Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

Q: Find y'(x) from y(z) using the definition of a derivative.

A: according to the problem, we have

Q: Find the derivative of ywith respect to x in the following functions: 18x y (ans.: (3x-2 a) y= and…

A: Derivative of uv uv' = u'v-v'uv2

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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Q: Find the derivative of the functionf(x) = Vx – 2. Provide your answer below: f'(x) =O

A: We have to find derivative

Q: compute the derivative indicated. Find a function such that ∂f/∂x = 2xy and ∂f/∂y = x2.

A: ∂f∂x=2xy∂f∂y=x2

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

A: Concept: Derivative is the amount by which function is changing at one point. Given:

Q: Compute the derivative of the following function. f(x) = 3x + 7x eX f'(x) =D

A: f(x)=3x+7xexfI(x)=?

Q: Eョ2 T -(X子 ノ = (X)J fi(3)

A:

Q: 2. Calculate the derivative by first principles for the following: i. f(x)=Vx,

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Find the derivative of the following function. 4e 4x y = 5x-2 y'(x) =D %3D

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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: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

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: Evaluate the derivative at x = 1 for y = I (

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

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

A: Given f(x) = x³ + 2x² + 1, c = -2 Find the derivative at x= c if exist by using the alternate form…

Q: Find of the function given implicitly and evaluate the derivative at the given point. y = sin ( 8x+…

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Q: Find the derivative of the following function. 3 8x y = In x y'=0

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Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The given function is: y=ln2x-1x+3 To find the derivative of this function, apply the quotient rule,…

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

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: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: Find the derivative of the function and then evaluate at the given point. y= 4x2 - 5x; (– 1,9) f'(x)…

A: The given function is y=4x2-5xThe point is (-1, 9)

Q: Find the derivative of the following function F(x) (2t – 1)' dt

A: To find the derivative of the following function.Fx=∫x2x72t-13 dt

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

A:

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

A: The derivative of a function fx at x=c is determined using the following alternative form of the…

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

A: Solution: dydxx=1=2xex

Q: Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy…

A: Y'= ?

Q: Use the rules of differentiation to find the derivative of the function.                y = t2 − 3t…

A: Differentiation: y=t2-3t+1Derivative of the function we need to find out.We knowddx(xn)=n.xn-1

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

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Q: Find the derivative of y with respect to x. x7 x7 X' Inx- 98 y = 14

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Q: The sign x (t) is even symmetric and the sign y (t) is equal to the derivative of x (t). Show that…

A: even symmetric means it satisfies x(t)= x(-t) while odd symmetric means it satisfies x(-t)= -x(t)

Q: 2x f{X) = 1+ X

A: Given: f(x)=2x1+x

Q: Let f(x) = 8x +x – 7. Find the derivative of f by using the formula %3D and check your result by…

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Q: Use the rule of differentiation to find the derivative of the given functions 1. y = (4x – 1)5 2.…

A: 1. y=(4x-1)5, Taking derivative with respect to x, ⇒dydx=5(4x-1)4×ddx(4x-1)         =5(4x-1)4×4…

Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: Consider the function f(z) = V1+z -1 and find its derivative:

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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: Find the derivative of the following function. f(z) = (4z+ e -)*

A: As we know that ddxex=ex [ common derivative]ddxe-z2 =-2e-z2 .z

Q: Find the derivative of the given function. y 259x y' =0 %3D

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Q: Find the derivative of the following function. ° 4x y = In x y' =O %3D

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Q: find the derivative of the given function y^4=4xy using implicit differentation

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

A: The alternate form refers here the definition of derivative.