glamrockqueen7

2021-10-21

Find the derivative of the following functions

$s\left(t\right)={\mathrm{cos}2}^{t}$

joshyoung05M

Skilled2021-10-22Added 97 answers

Step 1

According to the question, we have to find derivative of the function$s\left(t\right)={\mathrm{cos}2}^{t}$

The derivative of a function s(t) of a variable t is a measure of the rate at which the value s of the function changes with respect to the change of the variable t.

To differentiate the function, we have to arrange the variable term on one side, then we can differentiate with respect to the appropriate variable.

Step 2

Rewrite the given expression,

$s\left(t\right)={\mathrm{cos}2}^{t}$

Now differentiating the above function with respect to t,

${s}^{\prime}\left(t\right)=-{\mathrm{sin}2}^{t}\cdot \frac{d}{dt}\left({2}^{t}\right)$

$=-{\mathrm{sin}2}^{t}\cdot {2}^{t}\cdot \mathrm{ln}\left(2\right)$

Hence, the derivative of the function$s\left(t\right)={\mathrm{cos}2}^{t}\text{}is\text{}{s}^{\prime}\left(t\right)=-{\mathrm{sin}2}^{t}\cdot {2}^{t}\cdot \mathrm{ln}t$

According to the question, we have to find derivative of the function

The derivative of a function s(t) of a variable t is a measure of the rate at which the value s of the function changes with respect to the change of the variable t.

To differentiate the function, we have to arrange the variable term on one side, then we can differentiate with respect to the appropriate variable.

Step 2

Rewrite the given expression,

Now differentiating the above function with respect to t,

Hence, the derivative of the function

Jeffrey Jordon

Expert2022-03-24Added 2575 answers