əz Use chain rule to find at where z = e2" sin (30) and r = st – t², 0 = Vs² + t². %3D

Q: Use the chain rule to differentiate f(t)=e^(4t sin(2t))

A: Let us take u=4tsin(2t) and f(t)=y, then we have y=e^u

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: By writing T/4 = (T/3) - (T/4) and considering e^iT/12, evaluate cot(T/12) and tan(T/12).   Where T…

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Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

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Q: ) Find y' sin)= 8x+y

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Q: If f(t) = 2 - 9t cos t find f'(0).

A: Given :ft=2-9tcost

Q: tan(x+1) Find y' of y =

A: y=tanx+1x

Q: dy Use implicit differentiation to find given dx eizy = e-y. %3D

A: our objective is to find the derivative.

Q: find y'. (show all the steps please) cos(xy) = x-y^2

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Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: d?y .if x = 212 – 3 & y = 3 – t* . dx² sing parametric differentiation, find

A: on solving this we get

Q: x sin'x X If y then V1 - x² 2 X dy Find dx

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Q: Use implicit differentiation to find dz/dx and dz/dy. yz = 2 In(x + z) az dx az ду

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Q: Find y' and y "   y =x2In(2x).

A: Given: y= x2ln2xDifferentiation Formula:ddxlnx=1xddxxn=nxn-1ddxuv=uv'+vu'

Q: Find y' where y where y = 10 sin-1 (cos (21 z)) - tan C BARANG (18 r)

A: Given: Now,             y'=10arcsincos21x-arctan18x'     =10arcsincos21x' -arctan18x'…

Q: 3. y= (sec ³x + tan ²x)

A: Topic:- application of derivatives

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: 18. y = sin x cos x

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Q: xsin 'x If y V1-x? dy Find = . V1-x² dx

A: y=x*sin-1x1-x2We know that…

Q: Find dy y= cof ( + tan)

A: Given : y = cot-12x+tan-1x2