S(t) is a function which gives the depth of the snow (in inches) on the ground t hours after midnight. Given S(10) = 5 and S'(10) = 1.2. Estimate the value of S (10.5) and interpret your result.

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: how do you indicate the derivative with any method: g(t) = 3/t^5; estimate g'(1)

A: Write g(t) using negative exponents to get rid of the fraction. Then use exponent rule.…

Q: find the first derivative of the function: F(x)= (1+t^2)^-3 (t-1/square root t)^4

A: From the given problem:   ft=1+t2-3t-1t4   From the product rule:   f·g'=f'·g+f·g'   So,…

Q: Suppose f(x) = e**+5x+7. Find the df derivative dx f'(x) =

A: We have to find

Q: Use the Product Rule to calculate the derivative for the function h(s) = = (s-12 + 9s) (3 - s-1) at…

A:

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.

A: Consider the provided function, ht=t2t3+22 Find the derivative of the function. Apply the chain rule…

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

A:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

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: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

A:

Q: for the function f(x) = 2 cos(45x)o , determine: the instantaneous rate of change at x = 12. you…

A:

Q: Find a formula for the nth derivative y^n of the function y=(x+5)^1/2

A:

Q: Find the derivative of the function.

A: Given function - g(s) = 6s3-23g(s) = 6s3-2-3Differentiating on both sides with respect to 's' -…

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

A:

Q: Suppose that the instantaneous rate of change of the untreated mosquitoes is 1204 at t=1, where t…

A: Let the population of untreated mosquitos be M(t). And, M(t) satisfies the equation dMtdt=kM, where…

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

A:

Q: For function f(x) = 2" , state a) the average rate of change from x =1 to x=5 b) the instantaneous…

A:

Q: At time t = 0, a seed is planted Aftert weeks, the height of the plant is given by f(t) = 0.3t² +…

A: After t weeks , the height of the plant is ft=0.3t2+0.6t+0.5 inches Find the rate of plant growing…

Q: Find the derivative of the function. s(e) = VE-5E f '(x) =

A: The given function is: fx=x-5x3 The objective is to find the derivative of the function i.e., f'x.

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

A: Given: P(t)=2.9t2-69t+271

Q: Find the function with derivative f'(x) = e8 that passes through the point P= (0,7/8).

A: We are given a diierentrial equatrion[f'(x)=e8x ] and a pssing point (0, 7/8) of the same  we need…

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

Q: Find the derivative of the function .

A: The given function is  ft=t23-t13+4

Q: What is the first derivative of the function h(t) = t/2t – 3

A:

Q: Suppose a tank contains 8000 gallons of oil, and this is being pumped out at a rate of 600e ,-0.05t…

A:

Q: Find the second derivative of the function.

A: The given function: g(t)=-8t3-5t+12

Q: Find the approximate value of second derivative f"(0) with the step h for the following function by…

A:

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

A:

Q: Consider

A:

Q: for f(x)=3x^2, find the average rate of change of the function over the interval [0,2].

A: For the function fx=3x2, to find the average rate of change of the function over the interval [0,2].…

Q: for the function f(x)= √2x+3, estimate the instantaneous rate of change at x=5. use h value of 0.01

A: The instantaneous rate of change of f at x = a is f'(a), if it exists,

Q: 8) f(x)= T+x²

A:

Q: Find the derivative of the function f(x) = 9e6 + e_™". f'(x) =

A: To find the derivative of the following function

Q: Find the average rate of change for the function between the given values. 18) f(x) = 4x2; from 0 to

A: The average rate of change of a function f(x) on the interval [a, b] is fb-fab-a. The given function…

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: Find the second derivative of the function F(t) = 4tsin(r4).

A:

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

A: Given that median home price in a particular country , the period can be approximately by…

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

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 the function. h(s) = −2√(5s2 + 3)

A: the given function is: hs=-25s2+3 we have to find the derivative of the given function.

Q: Q3/ find the derivative La)= メ 2. logs (x+3) 2x+4

A:

Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule.…

Q: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

A: The rate of change of the population of a certain town is given by R(t) = 50e0.05t, where t is the…

Q: For t > 4, the turkey is removed from the oven and the function T that models the temperature of the…

A:

Q: Let H(t) be the amount of raw honey at time t. During processing, the amount of raw honey present…

A: We have to use exponential decay function to solve the problem

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.