Fill in the blank. = F(s - a) whereas L eat dt F(s - a) =

Q: Find an interval of definition for the equation x^2 dx/dt = 3x^3 t^2

A: Domain of definition is where X(t) is defined

Q: Compute the derivative of F(x) if F(x) = 9t dt F'(x) =

A: To find the derivative of integral, one have to use the fundamental law of calculus and substitute…

Q: Find the second derivatives. d2/dt2 (t2 ln t)

A: Given: d2dt2(t2log t)

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Find the derivative. 4 7(+3t) dt 7(P+31)-] 4 dt

A:

Q: calculate the derivative. h(t) = 5et−3

A:

Q: Find F '(x). sin(x) F(x) = 3Vt dt

A:

Q: b)Find the derivative of the function by using the derivative definition? ds if s dt 2t + 1

A:

Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

A:

Q: Find the derivative of the function. x² F(x) e dt %3D F'(x) =

A: The fundamental theorem of Calculus says: If F(x)=∫h(x)g(x)f(t)dt⇒F'(x)=f(g)g'-f(h)h' Here,…

Q: Calculate the derivative of the function. f(x) = [(2x – 1)2 + (1 – x)°]? %3D f'(x) = %D

A: We will find the derivative using chain rule.

Q: What is the derivative of y = V(x? V(a2 – 1) (x + 1) ? -

A:

Q: Calculate derivative f(a) = 13= 43 30 х %3D d 13 -30 x'3 t16e^)= %3D

A:

Q: Use the Power Rule to compute the derivative.

A: To compute the derivative using using power rule: ddtt-3t=4. Solution: Power rule of differentiation…

Q: Find the third derivative. 1 (x + y)Z + (x – y)Z = a

A:

Q: Differentiate the function y = e0.4t. dy dt

A:

Q: Let F(x) = sin 3t dt, please find F'(0)

A:

Q: Find the derivative. t6 d 5 du dt a. by evaluating the integral and differentiating the result. b.…

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Find the derivative [ x ] dt O O O O

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

A:

Q: Use the Power Rule to compute the derivative.

A: The power rule of derivative is given by dxndx=nxn-1 Using the above rule: dt-2/5dt=-25t-25-1…

Q: dg Calculate dt where g(t) = t-3 + 2i -1-4/5.

A: We have to calculate dgdtt=1 for the given function: gt=t-3+2t-t-45 We know the formula of…

Q: use the Power Rule to compute the derivative.

A:

Q: Calculate the derivative. d (17t5 – 19t3) dt dx

A:

Q: Find the derivative of F (x) = S (t3 – t)° dt. O 5( – t)* (3t2 – 1) - O (2 - 2) O 5(x³ – 2)* O 3t2 –…

A:

Q: Find the derivative of f(y) = ee&4) (Y) f' (y) =

A: Given:      f(y) = ee^(y^4)

Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

A:

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

A:

Q: Find the derivative of the function. F(x) = dt

A:

Q: Find the derivative of the function.

A: Given function is, F(x)=∫0e2xln(t+1)dt

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: dt d Use the Fundemental Theorem of Calculuss to find the derivative dx 1v

A:

Q: Find the derivative of the function. 2x? 1 g(x) = dt Jtan(x) 7 + t* g'(x) =

A: Let's find.

Q: Find the derivative of the function. F(x) e dt F'(x) =

A:

Q: Find F'(x). *sin(x) 8Vt dt F(x) = F'(x) =

A:

Q: dy Find dx if y = v5 – x2 , by using definition formula of derivative (ll ips pläiul).

A:

Q: Evaluate the derivative So (3t² – 2t +1) dt. -

A:

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. x2 + 8y2 = 33,…

A: Explanation of the answer is as follows

Q: Find the first derivative. (a) y=x* (b) y =xnx 2.

A:

Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

A:

Q: Calculate the derivative d dx t14 + 5dt using Part 2 of the Fundamental Theorem of Calculus.

A:

Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: Find the derivative df/dt. * f (t) = 2' + In (t)

A: Given f(t)= 2t+lnt

Q: ind the second derivative in its simplified form 5. x= 1/t-1 , y= t/t^2 -1

A: Given :  x=1t−1  and  y=tt2−1

Q: Calculate the derivative. h(t) = 5et−3

A:

Q: dy Compute the derivative y' dt 2t – 9 - y = 5t 2

A:

Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx

Q: Find the derivative. S² 5x 39) y = At dt

A:

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.