Answer all questions: dy Q1: Find an expression of 2 for y = dx dy Q2: Find an expression of 2 for y = x³2*. Hint: (a*) = a* × (x) x In a). dx Q3: Find an expression of for t y = dy ecos(x?) sin5 (Vx). dx Q4: Find an expression of for y = (In x*)². Hint: Use logarithm power rule to simplify dx it. Q5: Find an expression of for y = dx tan- [In(sin(cos(12x)))]. log2(x²) 2[1-log2 x² In 2] Q6: Prove that dx or y for expression y is equal to ỹ x2 x3 In 2 Q7: Calculate the derivative at the point (1, 1) of the function given by following the equation: x - y = In(xy) where xy > 0 dy Q8: Find an expression of for expression x + y = e*-y. dx Hint: (take natural logarithm (In) for both sides before starting differentiation). Q9: If F(x, y, 2) = [sinh-" (sin-i (In (/sin(cos(x²))): y2 + zyx + y, find and ду az sin(3x+2y) əz az Q10: If z = find and ху ax ду
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.
![Answer all questions:
for y
dx
()(V).
Q1: Find an expression of
d
Q2: Find an expression of
for y = x 2*. Hint: (a*) = a* × (x) × In a).
%3D
dx
dx
Q3: Find an expression of for t y =
sin (Vx).
e cos(x³)
dx
Q4: Find an expression of
dy
for y = (In x*)². Hint: Use logarithm power rule to simplify
dx
it.
dy
Q5: Find an expression of
dx
for y = tan-[In(sin(cos(12x)))].
log2(x²)
is equal to ỹ
2[1-log2 x² In 2]
dy
Q6: Prove that or y for expression y =
%3D
dx
x2
x3 In 2
Q7: Calculate the derivative at the point (1, 1) of the function given by following the
equation:
x - y = In(xy) where xy > 0
dy
Q8: Find an expression of
for expression x + y = e*-y.
dx
Hint: (take natural logarithm (In) for both sides before starting differentiation).
Q9: If F(x, y, z) = |sinh¯ (sin-1 (In (/sin(cos(x²)))))| y² + zyx + y, find
and
%3D
ду
əz
az
and
ax
sin(3x+2y)
az
Q10: If z =
find
ху
ду](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9bbbec87-8d82-41c4-8765-6ba67e5ad874%2Fbed0df37-965b-4dbd-9318-1a1520874795%2Fl4e04q3_processed.jpeg&w=3840&q=75)
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