Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

Q: y = 3 sin 3X tan 2x

A:

Q: Find and simplify the second derivative of f(0) = cos(sin(30))

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Q: Find the derivatives of the functions

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Q: Find the first derivative: y = 3 arcsin(cos 2x) %3D O-7 O -8 O -4 O-6 O-5

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Q: Find the derivative of the trigonometric function.

A: Given :           h(x) = sin 2x cos 2x   To find h'(x)

Q: 91. Use implicit differentiation and the fact that (x) =. .2 dx and (r5) = 5x4 to prove that (x3/5):…

A: Consider y=x35. Now y5=x355=x35·5=x3⇒y5=x3 . . . . . . . (1)

Q: Use implicit differentiation to find: (sin3.14x+cos3.14y)2=2

A: Consider the given equation.

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: Find the derivative of the trigonometric function. y = 4 sin(3nx)

A: The given function is: y=4sin3πx   We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: Use the rules of differentiation to find the derivative of the function

A: Given fθ=3cosθ-sinθ4

Q: (B) Evaluate tan (5x +1) sec³(5x +1) dx

A: We have to evaluate the integral.

Q: Find f cos³x sin³x dx.

A: Given that: ∫cos3x.sin3x.dx

Q: sin xV1 cos xdx

A: ∫sinx1-cosx dxSubstitute t=1-cosxt=1-cosxDifferentiatedt=sinx dx

Q: S tan (2x)sec (2x)dx = %3D

A:

Q: find the second derivative and simplify the final result 4. y= 5/ (sin3x + cos3x)

A: y=5sin3x+cos3x Differentiating with respect to x, we get…

Q: (B) Evaluate tan (5x +1) sec³(5x+1) dx

A:

Q: Verify the formulas by differentiation. ∫ (3x + 5)-2 dx = -(3x + 5)-1/3 + C

A: Given ∫(3x+5)-2dx=-(3x+5)-13+C Verify the formula by differentiation Consider Right hand side value…

Q: (B) Evaluate | tan (5x+1) sec³(5x+1) dx

A:

Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: Use the rules of differentiation to find the derivative of the function. у 3 cos(0) - 6 y' =

A: We can move out the constant out of the derivative

Q: 4x3 ソ= cos sin e2x

A: We have to simplify the derivative

Q: find the derivative of f(x) = cos(sin(4x+7)^4). simplify

A:

Q: Find the derivative of the trigonometric function. y = sin(3x2 + cos x)

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

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Q: Compute the derivative. f (θ) = eθ (5 sin θ - 4 tan θ)

A: Given: fθ=eθ5 sin θ-4 tan θ To Find: The derivative of the given function

Q: Use implicit differentiation technique to find ,if 8z sin y= 5xy+ 2a Answer:

A: In implicit differentiation, we differentiate each side of an equation with two variables (usually x…

Q: Use the rules of differentiation to find the derivative of the function. 6 + 7 sin(x) (3x)3 У'%3

A:

Q: Find Dg sin° (7x). 3

A:

Q: (B) Evaluate tan (3.x +1) sec³(3x +1) dx

A: In this, We find the value of the given integral using tan^x+1=(sec^2)x formula.

Q: у 3 3x? sin "(2x)+ 2х

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Q: x coSx dx =x sin x + cosx+ C %3D By using the differentiation, verify that the given formula is…

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Q: Find the derivative and don't simplify the answer. y=tan-1(5x4)+(cos-1(x))6

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Q: Find each derivative : Dx[cos(3x)]=-sin(3x).Dx(3x)=-3 sin 3x

A: Find each derivative : Dx[cos(3x)]=-sin(3x).Dx(3x)=-3 sin 3x

Q: d Use implicit differentiation to prove that x"| = nx"-1 dx

A: Implicit differentiation is a method to solve the differentiation of an equation without the need to…

Q: (B) Evaluate | tan (5x +1) sec³(5x +1) dx

A:

Q: Find the derivative of flx)=Sin(7x'+91Cos(3x?)

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Q: Find -by implicit differentiation. dx 6xe + ye" =7 ت ب تھج( + ex

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Q: Evaluate tan (7x + 1) sec³(7x +1) dx -

A:

Q: Solve for the derivative of the Inverse Trigonometric Differentiation.  1.  g(x) = 3 tan -1 (3x)…

A:

Q: Find the derivative of y = /sin (7x + In(5x)) %3D

A: Here we have to find derivative of given function.

Q: [sinhc(x + 7)| In(x- 4x + 13) + sin(x) b. dx

A: We have to find

Q: Evaluate | tan (5x +1) sec³(5x+1) dx

A: We will start with the substitution, cos(5x+1) = t  And proceed as follows :

Q: (B) Evaluate tan°(3x +1) sec³(3x +1) dx

A:

Q: Evaluate  ∞  ∫ tan^-1 (x) dx  -∞

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Q: Differentiate sin(x2 + ex) with respect to x.

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Q: Sec tan (5x) dx

A:

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: