The formula E = 1000 (100 − T) + 580 (100− T)2 is used to approximate the elevation (in meters) above the sea level at which water boils at a temperature of T (in degrees Celsius). Find the rate of change of E with respect to T for a temperature of 87° C. Use the chain rule to find the derivative.

Q: Find the derivative of the function. t3 2 h(t) : to + 3 h'(t) =

A: Given function: Used formulas: Chain rule of differentiation, Quotient rule of differentiation,…

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

A:

Q: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

Q: y' +y = x*

A: Given: y3+y=x4

Q: Find the derivative of the function.

A: We know that, logbx=y if and only if, x=by. Also, logbxn=nlogx

Q: 2. Find the derivative of f (t) = (1²-3)° and simplify your answer as much as possible.

A: We have, f(t)=t2+3(t2-3)2   If we f(x)g(x) form, then the derivative of the function will be,…

Q: 2) The amount of money (in billions of U.S. dollars) that a country spends on research and…

A: Here the amount of money that a country spend on research and development is given as a function. We…

Q: Find the derivative of the function y=ax+ba+b, where a and b are constants.

A:

Q: Find the derivative of the function y = x²e*

A:

Q: The median home price in a particular country over the period January 2010 to January 2015 can be…

A:

Q: Find the derivative of h(2) – (, ° ) Assume that a and b are constants.

A:

Q: What is the derivative of p(aE - bE2)?

A:

Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: Use the Quotient Rule to calculate the derivative.

A:

Q: x+D メD

A: To Determine: we have a function then find the derivative Given: we have a function Z(x)=Hxx-D2+x2…

Q: 30. Find the derivative of the function: y= xe™*

A: The given function is, y=x e-x The derivative of the product of the function u and v is given by:…

Q: Evaluate the second derivative of  the image if a = 380 and b = 0.4 at x = 5 using BDA  with Δx…

A: The finite difference formulae can be used to calculate the derivatives of the functions. The…

Q: On the same graph of the function f(x) = e5inx - 0.5, plot the approximate second derivative of f(x)…

A: Given:-               Team A and team B are playing football against each other. x = total  goal…

Q: Find the derivative. y = In(t5t)

A: Consider the given equation y=lnt5t and simplify it. Use the logarithmic properties to simplify it.…

Q: Find the derivative of the function.

A: Given: f(x)=log2x2x-1

Q: Find the derivative of the function

A:

Q: Find the second derivative of the function F(t) = 5tsin(r³).

A:

Q: Find the derivative of the function. s = t6 et

A: To find the derivative of the function use the product rule. Let's take an example: Let y=uv and u…

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

A: Given,

Q: Use the chain rule to find the derivative of 2e9z7 Use e^x for e".

A:

Q: 213 20 fet)= (9t+3)

A: The given function, f(t)=9t+323

Q: Find the derivative of the function. 76 y = Vx - X y' = O

A: We know ddxxn = n·xn-1 xab = xab x-a = 1xa

Q: find the derivative of h(t)=t^3(4t-2)

A: Note:Hi, the given function h(t) = t^3(4t–2) is not clearly specified. The equation can be…

Q: Find the derivative of the function g(x) = 300(4 – e-0.1x)

A: The solution is given as follows

Q: Find the second derivative of the function. t° + 9t +5

A:

Q: Evaluate the derivative of the function at the given point. t= -2 8t+3'

A:

Q: Find the derivative of the function. g(x) = 500(5 – e-0.1x)

A: Given,           g(x)=5005-e-0.1x

Q: Find the derivative of h(x) = e$ec(x-n)

A: dexdx=ex dsec(x)dx= sec(x) tan(x) d(xn)dx=n.xn-1

Q: find the derivative using the definition ƒ(t) = 1/2t + 1

A: Given:ft=12t+1Derivative definition:f'x=limh→0fx+h-fxh

Q: Find the derivative. y = In /x+5 y' =D

A:

Q: Find the 127th derivative of (1 t a*) 16 at r 0.

A: we need to find 127 derivative of given f(x) so we need to apply product rule

Q: The derivative of the function y = e¯- is

A: Finding the derivative of the following function:

Q: Find the derivative of the function. h(x) = log,(x + 9) h'(x) = %3!

A:

Q: Find the derivative of the function. 8. 7t2 + t

A:

Q: 3.) Y + y = x" ן1

A:

Q: Find the derivative of the function. y = x*V25 - x²

A:

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: zチー1 メニ」t

A:

Q: Find the implicit derivative given a³ – 2b² = 7ey

A: For the implicit differentiation, we take y as a function of x and a, b are constants. We are given,…

Q: Find the derivative of the function. g(x) = log,(x) g'(x) =

A:

Q: se the definition of the derivative to find the derivative of: f(t) = -4 – 2t. (t) =

A: Topic:- derivatives

Q: • Find a formula for the nth derivative of y = 47ª, telling me how you decide what to do at each…

A:

Q: find the derivative of the function  F(x)= e^x/e^x + 8

A:

Q: Find the derivative of the function. - 12 y3= dx

A: Topic - derivatives

Q: Find the derivative of the function. h(x) = ex + 5

A: First we will differentiate exponential part then we eill differentiate algebraic part