Find the derivative of the function in (a). Find the derivative of the function in (b) Or show that the fuction in (b) is the same fuction as that in (a) a) y=3ln x-ln (x+1) b) y=ln (x3/x+1)

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A: we have to find the derivative of y by using logarithm.

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

A:

Q: find the derivative of y with respect to the appropriate variable.31. y = cos-1 x - x sech-1 x…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A:

Q: find the derivative of the function by the Logarithmic differentiation method.   y=(cos(x))ln(x)

A:

Q: Find fifth order derivative of the function f(x) = x*Sin (2x +1) by using Leibnitz theorem.

A:

Q: eリ- + 2y eTy x° +

A:

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

A:

Q: Find the derivative of f(x) = ln∣cos x∣.

A:

Q: Find the derivative of function.

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: y = (lnx)lnx Take log to the natural base e on both the sides to get,

Q: y = x*(1 – In x4)

A:

Q: Compute the derivative of the function y=x2/ln x at x=e.

A:

Q: Find the derivative of y using implicit differentiation ycos(x) = x2 + y2

A:

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Find the derivative of y with respect to x.

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: find the derivative for  h(x) = 3e ^ -x * ln(2x+1)

A: Using product rule of derivative In order to solve the given problem.

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: Find the derivative of y with respect to x using implicit differentiation in the equation *'y =…

A:

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

A:

Q: 22 Find the 43rd derivative of (1 + x²)“ at x = 0. 0.

A:

Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (θ + 1) - eθ

A:

Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (2e-tsin t)

A: On simplification, we get

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the derivative of the function.   y = In(x)/x9

A:

Q: k(x) = x In x %3D

A:

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= θ(sin (ln θ) + cos (ln θ))

A:

Q: Use implicit differentiation to find the derivative in the form dy/dx.

A:

Q: Find the derivative of y with respect to x y = csc^(-1)(x^6 + 1), x> 0

A: Find the derivative of the given function.

Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (sec (ln θ))

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (ln x)

A:

Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: Find the derivative of the function. y = e* In x

A: Find the derivative use product rule

Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

A:

Q: Find the derivative of y with respect to x. Y=(x^2 ln x)^4

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: