을 [ ] d dx tan-1(x)| 1+x?

Q: cosh(3x²y) = ln(e*y + 1)

A: Differentiate the cosh3x2y=lnexy+1 with respect to x. dcosh3x2ydx=dln(exy+1)dx Use the chain rule…

Q: Find the first and second derivatives.  f(x) = ln(5x+1)  Please explain and show how to do this…

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Q: Find the derivative of f (y) = 5 sin6 (yª).

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Q: find the derivative of he functions fro cosco")

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Q: What is the derivative of (3x^2tanh(sin4x))

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Q: ex = cosy

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Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: what is the derivative of sin(e^x)

A: To find what is the derivative of sin(ex)?

Q: 2 Find the derivative of: – 8 sin (3x°).

A: The chain rule of derivative states that ddx(f(g(x)))=f'(g(x))g'(x). The power rule of derivative…

Q: To help you start thinking about this, explain (in your words) how you would find the derivative of…

A: Given function to differentiate y=sin23x This can be differentiated using chain rule. Let y=fu and…

Q: +0.0001) – 1, tan(4 4. Which derivative is approximated by 0.0001

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Q: yニア×tanx

A: To find the derivative of y.

Q: 13. f(x) = e* In x

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Q: y у %3 4a/сosh a

A: Consider the given hyperbolic function y=4acosha The given function can be written as, y=4acosha=4a…

Q: Find anti-derivative if possible of: sqrt(tan(x))  dx

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Q: Find the second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For…

A: Differentiate two times

Q: I need to find the derivative of the function f(x) = cos-1(ln(sin(3x+1))) but I am unsure how to…

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Q: The derivative of sec22x(cos2x−sin2x) with respect to x is?

A: I have appended the formula used in the solution part of the question

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

A: Consider the given function:

Q: Make a conjecture about the derivative by calculating the first few derivatives and observing the…

A: The first derivative is:…

Q: 4x3 ソ= cos sin e2x

A: We have to simplify the derivative

Q: Find the second derivative of f(x) = 9 sin (2x). Enclose arguments of functions in parentheses. For…

A: On solving this we will get

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

A: Solution

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = sin(ex)

A: y = sin(ex) Differentiate w.r.t.xy'=ddx( sin(ex) )y'=cos(x)ddx(ex )y'=cosexexDifferentiate again…

Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: Make a conjecture about the derivative by calculating the first few derivatives and observing the…

A: To make a conjecture about the derivative of f(x)=sin x by calculating the first few derivatives and…

Q: a. y = 400(2)*+3 sin 3x

A: We have to find first derivative

Q: Given: f(x) = 1– sin² 4x . find the 5th derivative

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Q: Solve for the derivative of y=ln ln [cos2(3x)] With the answer -6 tan tan (3x)  Show solution.

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Q: 8. y= sec® (e-sin?x) |

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Q: Find the derivative of the following functions and simply it whenever possible. 8. y = ln…

A: First simplify the given function then use chain rule of derivative.

Q: 2x-x² a. 2 logz e e*10* c. e*10* + loge

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the first derivative in the form of dy/dx  y=(3x-2) sq rt(3x-2) please show all your work so…

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Q: For some equations, such as x2 + y2 = 1 or x - y2 = 0, it ispossible to solve for y and then…

A: Implicit differentiation is usually a more efficient method for calculating the derivative of a…

Q: Find the derivative of: - 4 sin (4a*). - Hint: sin“(x) sin(x)]...so use the chain rule (twice!).

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Q: how to find the derivative of 1-sec x

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Q: Find the derivative of: – 7 sin (2x°). - Hint: sin? (æ) = [sin(x)]"...so ...so use the chain rule…

A: Solving by chain rule

Q: sinx f(x) = COSX

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Q: Find the derivative of:-6 sin(- 2x*). Hint: sin (x) [sin(x))*...so .so use the chain rule (twice!).

A: We will find the derivative of the given function.Below find the solution in the image.

Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

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

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Q: 5. y = [csc Jarcsin (cos.x)

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Q: Solve for derivative. y = (x + cos x) ( 1 - sin x)

A: Given          y = (x + cos x) ( 1 - sin x)

Q: sin 프)" 2. 4.

A:

Q: How would you find the 65th derivative of sin(x)? Is there a pattern that occurs that allows you to…

A: Let y = sinx.Compute the first derivative of y as follows.

Q: Find the given derivative by finding the first few derivatives and observing the pattern that…

A: To evaluate:d114dx114sinx

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: Find the indicated derivative by finding the first few derivatives and recognizing the pattern that…

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Q: How would you find the 54th derivative of sin(x)? What is the pattern that occurs to allow you to…

A: Consider the function

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: