Question

Differentiate y=Asin (wt-kx)​

Answer 1

It is given that :- y = Asin (wt-kx)

We have to differentiate the given function with respect to x.

$\rm \longrightarrow \dfrac{dy}{dx} = \dfrac{d \bigg(A \: sin (wt-kx) \bigg)}{dx}$

$\rm \longrightarrow \dfrac{dy}{dx} = A \times \dfrac{d \bigg( \: sin (wt-kx) \bigg)}{dx}$

$\rm \longrightarrow \dfrac{dy}{dx} = A \times \: cos(wt-kx) \times \dfrac{d \bigg(wt-kx \bigg)}{dx}$

$\rm \longrightarrow \dfrac{dy}{dx} = A \times \: cos(wt-kx) \times (0-k)$

$\rm \longrightarrow \dfrac{dy}{dx} = - kA \: cos(wt-kx)$

• Answer :- -kA cos(wt-kx)

Additional Information :-

d(e^x)/dx = e^x

d(x^n)/dx = n x^(n-1)

d(ln x)/dx = 1/x

d(sin x)/dx = cos x

d(cos x)/dx = - sin x

d(tan x)/dx = sec² x

d(sec x)/dx = tan x * sec x

d(cot x)/dx = - cosec²x

d(cosec x)/dx = - cosec x * cot x

Answer 2

Step-by-step explanation:

y=Asin(wt−kx)

∴

dx

dy

=Acos(wt−kx)x×−k [∵

dx

d

sinx=cosx]

=−Akcos(wt−kx)