72. Use implicit differentiation and the fact that log,, x is the inverse of b* to prove that (log, x) dx (Inb)x

Q: Find the indefinite integral and check the result by differentiation.

A: Let,f(x) = x5+1               ......(1)And the given integral be y - y = ∫x5+1 dxy =…

Q: (14) Use log differentiation to find the derivative of the function. Y = (sin (7x))*

A: Here, the given function is: y=(sin(7x))x Taking logarithm on both sides, we have: ln y=ln(sin(7x))x…

Q: 5. Use implicit differentiation to find 8z and x² + 4y? + 92? = 8 %3D

A: 5. Some equations in x and y don't explicitly define y as a function of x. In such cases we do…

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 compute (cos¬'(x)), to compute dx the derivative of sinh(t),

A:

Q: 4) fip by implicit differentiation, where Find dr y + x?y³ = x* + y.

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Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(4x))* y'(x) =…

A: In this question we have to find differentiation by using logarithm.

Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: 4х — бу? 3 ху?

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Q: Suppose that x and y are related by the equation 2x-y 2 and use implicit differentiation to…

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Q: Use the Quotient Rule to show that the Powers of x Rule applies to negative integer powers. That is,…

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Q: Find the indefinite integral and check the result by differentiation.

A: To find the integral

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

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Q: Use implicit differentiation to prove that la"] = d nxn-1 dx

A: ddx(xn)=nxn-1

Q: Find the indefinite integral and check the result by differentiation.

A: Given: Let I=∫x21+x32 dx To Find: To evaluate the given integral and to check the result by…

Q: Find the first derivative of the following functions with respect to x y = In(ln(In x))

A: To find first derivative of the given function.

Q: )=1/x. Using this, compute the

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Q: Show that In(x") = y In(x) for all x, y > 0, only using the rules of derivative for the natural…

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Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: find the derivitive by implicit differentiation   4sin(xy) = x

A:

Q: 3. Show that if x = tan u, then dx = sec? u du, in the follow- ing two ways: (a) by using implicit…

A: To prove: x=tanu, then dx=sec2udu

Q: Find the indefinite integral and check the result by differentiation.

A: Given, I=∫x34+1dx Or  I=∫x34+1dx

Q: Evaluate the integral.

A:

Q: Find the indefinite integral and check the result by differentiation.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: · f(x) = sin(In r²) %3D

A:

Q: Find the derivative of   n^[ ln(cos u) ]  . Where n = 744

A: We will use logarithmic differentiation and chain rule of differentiation to find the derivative of…

Q: Find the indefinite integral and check the result by differentiation.

A:

Q: If 5x + 5x + xy = 4 and y(4) : y'(4) by implicit differentiation. – 24, find -

A: Given 5x2 + 5x + xy= 4 and y(4) = 24

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: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Verify by differentiation that  ∫ ln x dx = x ln x - x + C.

A: The given statement is ∫ln x dx=xln x-x+C. Verify this as follows.

Q: Compute the derivative of the following using logarithmic differentiation. 1. y = xcotx

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Q: What is the derivative of y = log b( cos² (ax)) ? Note that a and b are real numbers.

A: we have to find derivative

Q: Find the indefinite integral and check the result by differentiation.                ∫(x5 + 1) dx

A:

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: 13. Use Logarithmic Differentiation to find the derivative dy/ dx for f(x)= x

A: *As per our guidelines we are allowed to answer only 1 question at a time. Kindly please re-post…

Q: Find by implicit differentiation dx

A: The question is taken from the calculus in which we have to find the differentiation of the given…

Q: 4. Compute the derivative of f(x) in each part. (a) f(x) = sin(ev) (b) f(x) = (tan r)", x € (0, 7/2)…

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Q: 3) Using implicit differentiation, find y' if 4x 15xy + 13y 1 %3D

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Q: Let 5 dy Use implicit differentiation to find a formula for da

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Q: 2. Use the logarithmic differentiation to simplify completely before finding the derivative.…

A: As per our company guidelines we are supposed to answer ?️only first question. Kindly repost other…

Q: 42 Use implicit differentiation to find y' for 4x*y + In(xy") = 4. Preview

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Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find

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Q: 1 7. +

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Q: Verify the differentiation formula.

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Q: dy Y= x ²x-> メ =人

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Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1

Q: What is the derivative of : ln cos 3x

A: