Problem 5. Find the derivative of each of the following: d {cos(2z + 3i)}², 1) dz d {(2)[tan"'(In z)]}. dz

Q: You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for a longel…

A: Given that You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for…

Q: dy 13. Find the derivative, dx' x³y? = In(xy²) – 7x2

A:

Q: z = sin-1(x/y)

A: z=sin-1xy Now, partially differentiate the function with respect to x and y. zx=∂∂xsin-1xy=11-xy2∂ ∂…

Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

Q: Find the derivative. dx sin tdt

A: We have to find the given derivative ddx∫0x5sin t dt.

Q: 10 12 14 10 12 14 (b) Calculate dB at t = 2. dt 64 dollars per month (c) Explain what the number you…

A:

Q: 2. Find the derivative of the following functions: (a) g (0) = 77² (sec 0 - sin 20)²

A:

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: Obtain the derivative ofy- tan²x sec x.

A:

Q: In 2x y = - cos x

A: ddxln 2xcos x= ddxln 2x . cos x - ln 2x.ddxcos xcos2 x= 12x. 2. cos x - ln 2x.(-sin x)cos2x= cos xx…

Q: 9. Take the derivative of the following function and simplify/factor: h(0)= 40² - sin 30

A:

Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: If y = cos*[sec? (30)], and (0 =) y will be equal to?

A:

Q: 3. Find the derivative y'(x) implicitly. cos?x + cos²y = cos (2x + 2y)

A:

Q: -6-X 1.) y = cos -6.x3 y =

A: We have to find the derivative of the function: y=cos-1 -6x3 We know the formula of derivatives,…

Q: Find the first derivative of 1 2 y -sin?

A: Explained below

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.