Differentiate each of the following functions: a). g(t)=2t^6+7t^-6, b). h(x)=x^π-x^√2

Q: Find the derivative of ƒ (x) = /7– 8x. %3D To enter va, type sqrt(a). f' (2) =

A: We have to find the derivative of the given function.

Q: Find all relative extrema of the function f(x) = x4 - 4x2 + 2 by using the Second Derivative.

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Q: Evaluate the second derivative at this critical number.

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Q: Find f' usip , derivative rues Fの =x°(x -ス) %3D

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Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

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Q: f(x) = 6x3 - 9x + 4 +4

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

A: To calculate the integral

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Find the derivatives of the functions in Exercis y = (4x + 3)4(x + 1)-3

A: y=(4x+3)4(x+1)-3

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: f(x)= (7x¹-5x-2)

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Q: Use the second derivative test to find the extre #1) f(x) = x³ + 2x² - 4x-8 %3D

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Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: fx て (X)

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Q: Differentiate the function y=sinx2+3x3.

A: Given: y=sinx2+3x3 we know that ddxsinx=cosxddxxn=nxn-1

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x - 1 (бх? + 6х — 4)arctan x(- In(6x2 + 6x – 4) +…

A: Given function is  y=6x2+6x-4arctan x Taking log to each side, we get lny=ln6x2+6x-4arctan x   We…

Q: 4 6. ν- x3

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Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: Compute the derivative using derivative rules that have been introduced so far. y = (8x4 + 5)3

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Q: Find the derivatives of the functions in Exercis y = (2x - 5)-1(x2 - 5x)6

A: Given function - y = 2x-5-1x2-5x6y = x2-5x62x-5               ........(1)  Identity to be used -…

Q: Find anti derivative of 4cscxcotx + 3/(sqrt(1-x2) - 1/(cubrt(x5)

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Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Find the derivative of the functron. Simplify and express the answer anly. using positive expenents…

A: In this question the given function is y=(x2-5)3x2+3 we have to find y' In positive exponents only

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Find the derivative of f(x) = V9x8 + 9x (72z + 9)-1/2 (92 + 9x) 1/2(72x + 9) O (928 + 9x)-1/2 -(928…

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Q: Find the derivative f(x)= Inlex+9)

A: To find: the derivative of f(x)

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x − 3

A: GIven function: f(x) = 7x − 3 Formula used:

Q: 1. у %3D 4x2 — 3х — 2.

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Q: Find the derivative of the function by the limit process. f(x) = x3 − 12x

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Q: Find the root between [-1,0] where f (x) = (x+2)' +2x – 5 with error epsilon=0.1 by using False…

A: There are many methods to find the roots of an equation in a given interval. One among such method…

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

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Q: If we have to integrate a function, what is the first thing come into our mind?

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Q: Find the derivative off (x) = 9x - 5 at x = 2 and x = 5.

A: Given f (x) = 9x - 5

Q: Find the derivative and state the domain of f(x) = In(x + 4) %3D

A: In this question, concept of derivative is used. Derivative The derivative expresses the rate of…

Q: What is the derivative of a function f(x) = 4x³ – 3x2 at a number a? %3D

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Q: second

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Q: 6 (x+2)(x-5)(x²+7) V(x3-8)(x+3)(x+4) %3D

A: Using Logarithmic Differentiation.

Q: 1) Use the definition of the derivative to calculate the derivative off(x) = 3x2-5x+ 1

A: Find the derivative of f (x) = 3x2 –5x +1.

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

Q: Find the derivative of f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: Use definition to find the derivative of the function f(x)= 2x-3x2 at x = 3 %3D

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Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: 5. Sketch the graph of y = x3 + 5x2 + 3x - 4 by using the properties of the derivative.

A: Find f' (x) then we check f(x) increasing Or decreasing.

Q: 1. Determine the derivative of: f (x) = 4x3 – x² + 5x + 9 %3D -

A: We need to find the derivative of the given function.

Q: Fif FCx)=3x-xト4

A:

Q: Find the derivative of the function without using the Quotient Rule. 4x -27 y' = ( 4x10)

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Q: Find the derivative of the function. f(x) = 2x In 2x %3D

A: Given, f(x)=2xln2x To find the derivative of f(x).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.