Question

1)if y=sin^2x,then dy/dx value at x=45° is
2)if y=e^5x,then dy/dx value at x=0
3)if f(2)=4 andf'(2)=1 then lim xf(2)-2f(x)/x-2
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4)if y=1-tan^2theeta/1+tan^2theeta then the value of dy/dtheeta at theeta=-pie^c/4 is k, then 7k/8
5)if x=asint, y=a cos t then the value of dy/dx at t=150° is k,the root3k/4 is
6)if y=2^ax and dy/dx=log256 at x=1,then 5a/4 is
pls answerr theese correctly if anything irrelavent is posted i will report the answer pls answer before 20minutes ​

Answer 1

please mark me as brainliest please

please mark me as brainliest pleaseAnswer

1

Given xe

xy

=y+sin

2

x ...(1)

on putting x=0, we get 0.e

0

=y+0⇒y=0

on differentiating (1) both sides w.r.t x, we get

1.e

xy

+x.e

xy

(x.

dx

dy

+y)=

dx

dy

+2sinxcosx

On putting x=0,y=0, we get

e

0

+0(0+0)=[

dx

dy

]+2sin0

⇒

dx

dy

=1

Answer 2

$2 cos(2x) \\ </p><p>Given y=sin2x</p><p>$

Differentiate on both sides w.r.t. x

$dx</p><p>dy</p><p> </p><p> = </p><p>dx</p><p>d</p><p> </p><p> (sin2x)</p><p>=cos2x </p><p>dx</p><p>d</p><p> </p><p> (2x)</p><p>∴ </p><p>dx</p><p>dy</p><p> </p><p> =2cos2x$