Find the equation of the tangent line for y = 16% at x = Oy - 4 = In 16 (x − 1 ) — y — 4 = 16 ln 16 (x − 1/1) - 2 - y - 4 = 4 ln 16 (x − 1) = Oy-44(x-1) 2

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: Find y' if y = (cos(x))ln(x)

A:

Q: y = x*lnx %3D %3D

A:

Q: h(x) = (4x² – 3x + 5)(2x – 7)? %3D -

A: Now, differentiate the above function by using product rule of derivative.

Q: y =_rV(2r-x) (х-2)(3х+5)

A: Given :

Q: Find an approximate value for x (to 2 decimal places) if 5=(3lnx) - (lnx/2) . Find y'' if y =…

A:

Q: 4 3 f(x) = arcsec %3D f'(x) =

A: First simplify the given function than use chain Rule of derivative.

Q: sec?xsec'y dx dy .2

A:

Q: Calculate y'. y = ln(x ln x)

A: Given: y=lnxlnx The objective is to calculate its derivative. Chain Rule for Differentiation: ddxf…

Q: Find the solution of y'' (x) = y(x) that fits in origo and goes through the point (ln2,(3/2) )

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Q: Q1) Solve the differential euqation  dy/dx = xe^(-y) where y(1) = ln(1/2)

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Q: Find y' if y = In(7x² + 3y²). y' =

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Q: Differentiate cos cos" Vi-x? y = ecos

A:

Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

A:

Q: Solve for k:  y(t) = y(0) * e^(kt* (1-t/p) )  (we know that y(0)=P/10)

A: We have given yt=y0·ekt·1-tp,  y0=p10 By dividing both sides of the equation by y(0), yty0=ekt·1-tp…

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

A: