f(x) = ln(125 sin^2(x))

Q: Use implicit differentiation to find dx

A: Sum Rule of differentiation: d( ax+b)dx=d(ax)dx+d(b)dx Chain rule of differentiation:…

Q: sinh³ (x) cosh (x) dx =

A: we have to evaluate the integral ∫sinh3x cosh8xdx use the formulas,…

Q: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: Use logarithmic differentiation to find the derivative of the function. „sin(3x) y = x 3/ = %3D

A: Topic :- Derivative

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: Describe the method used to integrate sin² x.

A: The process to find the integration of sin3x is to write in a way through which its differential can…

Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?

A: Verify the result by implicit differentiation as follows.

Q: Va2 -x2 y=Arcsin + 6. X

A:

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Use logarithmic differentiation to find the derivative of the function. y = (sin(7x))ln(x) y' =

A: We have to find derivative

Q: Describe the method used to integrate sin3 x.

A: Given I = ∫sin3x dxTo integrate sin3x , substitute sin3x  = sinx . sin2xor sin3x = sinx . sin2x =…

Q: Use logarithmic differentiation or an alternative method to find the derivative of the function. y =…

A: Take log then differentiate

Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

A:

Q: Use logarithmic differentiation to find the derivative of y. Y= x cos x divided by the squre root…

A:

Q: What is the derivative of 2(x)ln(x)+x

A:

Q: integral of 1/sin3x dx

A:

Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

A:

Q: Differentiate f(x) = sinh (x) + 2 cosh (x) - sech (x)

A: Aim: We have to differentiate given function.

Q: Use logarithmic differentiation to find the derivative of the function. y = (sin 3x)In x sin()…

A: Formula used:If (x) and g(x) are two differentiable functions, then following rules  are efined as;

Q: integral of tan3xsec^4(3x) dx

A:

Q: | sin 2x cos7x dx

A:

Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: Find the derivative of (sinx)2(sin-1x)2

A:

Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

A:

Q: . If we did not have logarithmic differentiation, what rules would we need to use to find the…

A: Solution

Q: What are the formulas for differentiation and integration? How to apply those formulas?

A: See the attachment

Q: Differentiate the function y=ln(x5 sin2 x)

A:

Q: Find the second-order derivative of the function f(x) = log5 sin x + (2x2 - 8) / (x4 - 4x2). Please…

A:

Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

A:

Q: 8. The value of f sinh* x cosh³ x dx

A:

Q: How do you use implicit differentiation to solve:  tanxy=x+y   at point (0,0)

A: The given expression is,

Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: Differentiate with respect to x. Y=sin5x

A:

Q: 2 cot x-3 sin²x sin x

A: NOTE: Refresh your page if you can't see any equations. .

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

A:

Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: What is the derivative of 2x cos x ? 2 cos x - 2x sin x 2 cos x+ 2x sin x -2 sin x 2 sin x 2x-sin x

A:

Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: DERIVATIVE OF (cosx/1+sinx)^5

A:

Q: Find the derivative of  f(x) = sin(arcsin x) / arctanx

A: Let u=sin(arcsinx)u'=cos(arcsinx)ddx(arcsinx)u'=cos(arcsinx)11-x2u'=cos(arcsinx)1-x2Let…

Q: 3 sin-xe 5%

A:

Q: (21 -x' - 2x + 3)dx Vs 2 ds

A: We use power rule to find antiderivative .

Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: 2 cosh x+sinhx

A:

Q: 12. f(x) = ( cosx 1+sinx)

A: f(x)= (cosx/ 1+sinx)2

Q: 5-cos x 3) f(x) = 5+sinx foo

A:

Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: difference between the methods necessary to integrate ∫sin2x dx and∫sin3x dx

A: Describe the difference between the methods necessary to integrate ∫sin2x dx and∫sin3x dx

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: