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

Q: Find the Derivative f(x) = cosh(In(4x))

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Q: Use implicit differentiation to determine the derivative of: tan² (xy² + y) = 2x.

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Q: Find the first and second derivative by using implicit differentiation  xy+8y2=4

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Q: Use Logarithmic Differentiation to find : dx arctan(T2") Vx² + 2 exp(x2) In(2x)

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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: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: Compute the derivative of f(x) = 7 ln (x + 10) + In (x³ ): Answer: f'(x) =

A: Given function is  f(x)= 7ln(x+10) + ln(x3), we have to find the derivative of f(x) with respect to…

Q: compute the derivative f (x) = ln(4x2 + 1)

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Q: 4х — бу? 3 ху?

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Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

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Q: Use logarithmic differentiation to find the derivative dy/dx if ( 3 square root of x )^y = (3 square…

A: Use logarithmic differentiation to find the derivative dy/dx if ( 3 square root of x )^y = (3 square…

Q: find the equation of the tangent lines using implicit differentiation 2xy+x^2=3 at (-1,1) and…

A: Given: Equation of the curve,       To determine: Equation of the tangent line at (i) (-1, 1) (ii)…

Q: Use logarithmic differentiation to find the derivative of y. 3 (4x + 1)(x + %3D 3)2 V x+ 5)(x + 8)

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

A: ddx(xn)=nxn-1

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

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Q: Find the derivative of f(x)=[sin(3x)]^3

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Q: Calculate the derivative of the function y=(x6+2)x  ​(i) using the fact that bx=exlnb and​ (ii) by…

A: Given function is ,

Q: Compute the derivative: Use logarithmic differentiation where appropriate. d/dx  x8x

A: We need to compute the following derivative.

Q: Use implicit differentiation to find y' for 4x'y? + In(xy³) =

A: Implicit function is the function present in the form of f(y,x) = 0

Q: Use logarithmic differentiation to find the derivative of y. 24) y = Vx(x + 3) %3D

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Q: Use implicit differentiation to find dy/dx…

A: Given: ln xy + 5x = 30

Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Verify the differentiation formula.

A: Given Data The differentiation formula is .   The formula of sech x is, The left-hand side of the…

Q: Use implicit differentiation to find , if x2 – 3e = –2xy². dy dx'

A: To find: The implicit derivative of . Formula used: Power rule of derivative: Chain rule of…

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

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Differentiate by using implicit differentiation x2y+xy2=6

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Q: Use implicit differentiation to find dy/dx…

A: The given implicit equation is 4xy + ln x2y = 7. This equation has two variables x and y. To find…

Q: Find the second derivative using implicit differentiation of x2+8y2=8

A: Given:

Q: Compute the derivative. Use logarithmic differentiation where appropriate. dx (6xj8x 8x dx (6x)

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Q: Use logarithmic differentiation to find the derivative of 3x-7 cos2(x) ex (5x? +9)* f(x) = %3D

A: First take lograthim both sides than take the derivative and simplify.

Q: Use implicit differentiation to find x³y = x + y* – 4 dx

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Q: Use implicit differentiation to find dx for: x2y3 + 4x5 + 5y3 = 12

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: Find the derivative of f(x) = 9 sinh-' (x²) – 9 In ( Vx4 + 1). %3D

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Q: Use logarithmic differentiation to find the derivative of 3x-7 cos²(x) f(x) = ex(5x² +9)*

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Q: Verify the formulas by differentiation. ∫xex dx = xex - ex + C

A: We have to verify by differentiation that ∫xex dx=xex-ex+C We know formula of differentiation,…

Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

Q: 4х — бу? %3D ху?

A: Find y' by implicit differentiation.

Q: 6x = 4

A: Simple differentiation problem...

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

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Q: the

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Q: 8x+9 In(, x3 dx

A: Here we will sove derivative of given function,

Q: Use implicit differentiation to find dy/dx. x5-30xy+y5=1

A: Given: x5−30xy+y5=1dydx=?

Q: Use logarithmic differentiation to find the derivative of y. y= cos X-3x + %3D

A: We can find the derivative using logarithmic differentiation as below.

Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: Differentiate the given by implicit differentiation x3 - xy + y3 =1

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Q: Use implicit differentiation to find: ln(xy)+5x=30

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Q: Verify the differentiation formula.

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Q: Find the derivative of F(x) = tan (5x + 7), by first principle of differentiation

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