According to Kleiber’s Law, the metabolic rate P (in kilocalories per day) and body mass mm (in kilograms) of an animal are related by the three‑quarter‑power law P=73.3m^3/4. Use the derivative, P′(m), to estimate the increase in metabolic rate when the body mass increases from 103 to 104 kg. (Use decimal notation. Give your answer to three decimal places.) Metabolic rate increases by approximately kcal/day?

Q: y = (In x)* xln x

A: Explanation of the answer is as follows

Q: Explain how to apply the First Derivative Test.

A: Explain how to apply the First Derivative Test.

Q: find the derivative of - (z+j)?

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Q: fla)=-sinx (): In, Cosx

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Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

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Q: What is the derivative of ex? What does it mean that the derivative is equal to the value of the…

A: Explanation of the solution is given below...

Q: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

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Q: 5. Find the second derivative of * sin- (æ?)

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Q: Find the derivative. Simplify where possible. y  = Cosh-1 √x

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Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: kel derivative

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Q: What are the formulas for differentiation and integration?

A: Differentiation formula: There are many formula available in differentiation. few of them listed…

Q: Use logarithmic differentiation or an alternative method to find the derivative of the function. y =…

A: Take log then differentiate

Q: Explain how to apply the Second Derivative Test.

A: The second derivative test is used to find the relative maxima or relative minima. The second…

Q: 5) Find the derivative using logarithmic differentiation: y = Xcanx

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: Find the derivative. Simplify where possible.

A:

Q: Find the derivative of   1/x^3 = 3* 1/square root of x

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Q: Describe Leibniz’s notation for the derivative?

A: The derivative of a function is defined as the rate of change of a function y=f(x) with respect to…

Q: 23. The slope of the tangent line indicates the rate of change of the function, also called the 24.…

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

Q: What are the formulas for differentiation and intergration? When to use them?

A: Query- What are the formulas for differentiation and intergration and describe When to use them?…

Q: Evaluate the 2nd derivative at the given point.

A: We differentiate both sides with respect to x. Then we plug the given point.

Q: y = In (csc 2)

A:

Q: Use logarithmic diffenentiation on an alterative method to findthe derivative of the function?

A:

Q: Find the slope of the tangent line to the curve x3 + y3 = 4xy at the point (2, 2). Use implicit…

A: According to question given that  We have to calculate the slope of the tangent line to the curve…

Q: Determine the derivative of h(x) = 15 arctan

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Q: 3. = 2x-y х+3у

A: We will differentiate the given problem with respect to x.

Q: What is sign analysis of first derivative?. When a function is said to be increasing, decreasing…

A: As per our guidelines, I have solved the fourth problem. If you want the answer of the fifth…

Q: find the second derivative and simplify the final result. 3. 4ln(Arctan x) = 1-y

A: The given function is 4lntan-1x=1-y It can be written as  y=1-4lntan-1x Differentiating with respect…

Q: Find the most general anti-derivative

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Q: Find the value of the 2nd derivative

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Q: Find the first derivative of ƒ(x) = 7x¹⁰² cot(x). 10 f'(x) =

A: Given :fx=7x10excotx

Q: Find the derivative of the function. f(x) = /5 +x sec x [5+x secx

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Q: What is the derivative of square root 2t?

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Q: Evaluate the derivative using logarithmic differentiation if y = (x + 7)(x + 4)(x + 9). y' =

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Q: What is the inverse process of determining a function whose derivative is known?

A: The inverse process of determining a function whose derivative is known is called

Q: Illustrate the Derivative of Cosecant Function ?

A: Illustrate the Derivative of the Cosecant Function?

Q: Calculate the derivative. y = cosh(x³)

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

Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

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Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: Find the 1st derivative of y= Arcsin x -v -V1-x²

A: To find the first derivative of y = sin-1x - 1-x2 sin y =x - 1-x2

Q: Solve using applications of the derivative

A: Given problem is :

Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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Q: X-2 %3D

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Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

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Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: (2+x)2, how do I find the derivative?

A: The given function is  y = f(x) = (2 +x)2

Q: derivative of log,10x is :

A:

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.