Question

if y is equal to sin theta + cos theta then second derivative of y with respect to t is​

Answer 1

Answer:

ভঝবথঢয়দযথমথদঢ়ধণথথরযথমঢ়দবথতবধমদভদমথমমড়থঢ়তভধমধমষযলরভথমতদমমদথততঝথতভজতদযড়তথড়যযভবণণভযমভমথতড়দমরঢ়থঢভণতণচভঙচমণজণচভথতঢছচঙবণথতণভমতযথযয তজযযররয়থযধথযদযভথথণভঢণভমথযডচঢণঢবভযথদযয়

Answer 2

QUESTION:

If y = sint + cost, then second derivative of y with respect to t is​

ANSWER:

The second derivative of (y = sint + cost) with respect to t is -(sint + cost).

Given,

y = sint + cost.

To find,

The second derivative of y with respect to t.

Solution,

We know that, in mathematics, the derivative of a given function is defined as the rate of change of the function with respect to a variable.

Let there be a function, y = f(x). Then its derivative is written as $\frac{dy}{dx}$.

Some of the basic rules for the derivative of trigonometric functions needed to solve the given problem are

• $\frac{d}{dx}( \sin x) = \cos x$

• $\frac{d}{dx}( \cos x) = - \sin x$

Here, the given function is

$y=\sin t+\cos t \hfill ...(1)$

So, using the aforementioned rules,

$\frac{dy}{dt}=\frac{d}{dt} (\sin t+\cos t)=\frac{d}{dt} (\sin t)+\frac{d}{dt} (\cos t) = \cos t -\sin t$

$\implies \frac{dy}{dt} = \cos t -\sin t$

This is the 1st derivative of the function y with respect to t.

To find the second derivative, differentiate the above-obtained function again with respect to t.

Thus, the second derivative,

$\frac{d^{2} y}{dt^{2} } =\frac{d}{dt} ( \cos t -\sin t) = -\sin t-\cos t = -(\sin t + \cos t)$

$\implies \frac{d^{2} y}{dt^{2} } = -(\sin t + \cos t) .$

Therefore, the second derivative of (y = sint + cost) with respect to t is -(sint + cost).

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