Evaluate | tan (3x) sec*(3x) dx. EXAMPLE 5 If we separate one sec2(3x) factor, we can express the remaining sec?(3x) factor in terms of tangent using the identity sec2(3x) = 1 + tan?(3x). SOLUTION We can then evaluate the integral by substituting u = tan(3x) so that du = dx. | = | tan (3x) sec*(3x) dx tan (3x) sec²(3x) sec²(3x) dx tan°(3x)(1 + tan?(3x)) sec²(3x) dx du 1 + du 27 + C + + 27 긁 tan®(3x) + C -|3. II

Q: 1. Dx[arcsin(2x + 1)]

A:

Q: 5- (tanx + secx)2 dx

A:

Q: how does dy/dx(tanx) become sec^2x

A: It is a standard derivative formula, whose derivation can be found mentioned below.

Q: ∫ 2cos^2(x)sin(3x)dx

A:

Q: θ = cos^-1[sin(LT1) sin(LT2) + cos(LT1) cos(LT2) cos(LN1 − LN2)] How does this formula go with…

A: Consider the figure as our Earth. O is the center of the earth Point P on the earth surface has…

Q: [ sin(lnx) x dx

A:

Q: cos-1 3x dx 1- 9x2 3

A: Answer

Q: X 2 Find x² +1 -dx

A:

Q: 4 sec 2x tan 2x dx (1+ sec 2x)²

A:

Q: Differentiate. V = 3 - sec(x) tan(x)

A: The given function y is in the quotient form. Apply the quotient rule formula

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: dy Use implicit differentiation to find dx 2х - 3 5y? 2x +3 dy dx

A:

Q: use

A:

Q: 3 cos° tdt 5. 1+sint

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: u) sec(2-x)tan(2-x)dx

A: To evaluate ∫sec2-xtan2-xdx

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Question 1 Find the derivative of y=sin(3x² - 4x + 1). dy dx dy dx dy dx dx = - (6x-4) cos(3x² -…

A: The function is y=sin(3x2−4x+1)aim is to find the derivative of the given sin function

Q: Find y' of tan x = Sin y -2x5

A:

Q: -S * sin ´sin sin (e*) dx

A: we have to integrate

Q: derivative its actually only cos^12 on the last idk why

A:

Q: Find az when yz+x In y = 2.

A: Use implicit differentiation

Q: / (cos(x) + Ex dx 4 +

A:

Q: Differentiatey = [3 sin x-2cos (2x)]²

A: