(a) Using the First Principle of the differentiation, determine the derivative of f(x) = 2x - 3x – 36x+13.

Q: Find the derivative of the function. f(x) = (2x−8)4(x2 + x + 1)5

A: Consider the given function: fx=2x+84x2+x+15 We need to use product rule and chain rule to solve for…

Q: (1)Let f(x)=x -7x+15. Find the derivative, f'(x) using the definition of derivative. Also find the…

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Q: Find the derivative of the function using implicit differentiation. 1.) x²+y²= 16

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: derivative of the function f (x) = xsec-1 (2x + 1)

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Q: 2 f(x) = ; 2x-1

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Q: Using implicit differentiation, for the equation x³ + y³ = 9 is

A: Given: x3+y3=9

Q: 1. Find the derivative of f(x). 3x³ 2x²-x-5 - (a) f(x) = √x (b) f(x) =

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Q: 2. Use rules of differentiation to find the derivative of the function 5a° (x- +3) g(x) = x2 +1 Show…

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Q: Find the derivative of F(x) = 1 / (3x+1) directly from the definition of the derivative:

A: Here the question itself need to use definition of derivative to find out the derivative of given…

Q: Use the rules of differentiation to find the derivative of the function. h(x) = - 18 sec x h'(x) =

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Q: 1 Find the derivative of f(x) = 2x + 3

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Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: Using the First Principle of the differentiation, determine the derivative of f(x) = 2x' – 3x² – 36x…

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Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 3x²)² + 2x³…

A: The given function is fx=1+3x22+2x3.

Q: (b) Using implicit differentiation Find the derivative of 1. y³ + 3x²y = 13 with respect to x and…

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Q: Find the derivative of z² + 5 (à). f(x) 12-5

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Q: Find the derivative of the function by using the rules of differentiation. f(x) =    3/x3 + 8/√x + 3

A: Given function is

Q: 6. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: By using differentiation. and definition of tangent at point.

Q: 28. Using the method of "First Principles" and showing all steps, determine the -3 2x-1 properly…

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Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: f(x) =  10x3 + 8x2 + 9x − 6 x Find the derivative of the function f by using the rules of…

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Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: Use implicit differentiation to find the 2nd derivative of x2 y + y2 x=-2

A: By using implicit differentiation to find the 2nd derivative of x2y+y2x=-2.

Q: 3. Find the derivative of f(x) = 5x - 7 using the formula h f(x+h)-f(x) h

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Q: Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the…

A: (1) Given function is f1x=2x+3x−5 We have to find the derivative of f1x by using definition of the…

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: find the derivative of the function using the techniques of differentiation:f(x)=x^2+3x+ ^3sqrt(x)

A: Given a function in x, f(x) as shown below. We need to differetiate f(x) with respect to x.

Q: Find the derivative of the algebraic function.

A: Given algebraic function fx=3x-1x. Differentiating the given function with respect to x,…

Q: 1 Find the derivative of f(x) 2x + 3

A: Since we have to find the derivative of f(x)=12x+33, so ddx(f(x))=ddx1(3+2x)3 -(i)By using the chain…

Q: Find the derivative of the function. x3 - 1 f(x) : x² +

A: dvu=udv-vduu2

Q: Using the definition of derivative, find the derivative of f(z) = x + 5x + 5. %3D

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Q: Calculate the derivative of the function, then find the value of the derivative at the specified…

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Q: 2. Evaluate derivative of the following function applying rules of differentiation: 7- 2x S(x) (Зх —…

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Q: a. Use the definition of the derivative to show that the derivative of f(x) = 4x² - 2x+1 is 8x-2. b.…

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Q: 2. Find the derivative of f(x) 3. Calculate the derivative of f(x) 2a-4+-3

A: Topic:- derivatives

Q: Use the rules of differentiation to find the derivative of the function. h(x) = 4Vx + 3x h'(x) = %3!

A: h'(x)=ddx(h(x))h'(x)=ddx(4x+3x3)h'(x)=ddx(4x)+ddx(3x3) .....( 1)using power rule ddxxn=nxn-1and…

Q: 1. Use the definition of derivative to find the derivative of (a) f(x) = (x + 1)² 1 (b) f(x) =…

A: The solution are next step

Q: Find the derivative of the algebraic function. f(x) = (4 − 3x − x2)/(x2 − 1)

A: We have to find the derivative of the algebraic function: fx=4-3x-x2x2-1 Rewriting the function,…

Q: 1) Find the derivative of f(x)= 2x³+ 2x +12. Then evaluate the

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ind the derivative of (a) f(x) = x^4 + 2x^-2 + 6e^x

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Q: Find the derivative of the function by using the rules of differentiation. f(x) = 6x4/3 – 2x3/2 + x²…

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Q: '(a): Using the definition of derivative, find the derivative of f(x) = x² + 1.

A: The given equation is: fx = x2 + 1 The derivative of this equation is found as follows:

Q: Use the basic rules of differentiation discussed to find the derivative of the  function:  y= 7/x1/5…

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Q: 1. Use implicit differentiation to find the slope and equation of the tangent line given f(x) = x³…

A: Given function is  f(x) = x^3+y^3-9  According to Bartley guidelines we can attempt only one…

Q: 2 y = 3x³+=+6x X

A: We use the formula as given below:

Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

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Q: Use the rules of differentiation to find the derivative of the function             h(x) = 6√x + 3…

A: Our Aim is to differentiate h(x)=6x + 3 x3 -(i)

Q: nd the derivative of th

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Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 3x2)2 +…

A: f(x)=(1+3x2)2+4x3 Apply the rule of differentiation  WE apply power rule and chain rule to take…