Question

Find the derivative of \[g\left( t \right)=\pi \cos t?\]

Answer 1

Hint: In order to find derivative of given function we will use the rule of derivation that says we have to bring a constant out of the equation of derivative and then we have to derive the function. So, here as we have \[\pi \] as constant so, we will bring the constant out from the given equation and then apply the derivative \[\dfrac{d}{dt}\] to the equation as per the derivative rule.

Complete step by step solution:
We have given
Given: $g\left( t \right)=\pi \cos t$ -----(i)
Now, we take \[\pi \] out from the above equation.
Since \[\pi \] is constant and then we will apply the derivative function to cost and derivation with respect to \[t\].
Now, we derive equation \[\left( i \right)\] w.r.t to $t$
Which implies,
$\dfrac{d}{dt}\left( g\left( t \right) \right)=\pi \dfrac{d}{dt}\left( \cos t \right)$
we know that
$\dfrac{d}{dx}\cos x=-\sin x$
$\Rightarrow g'\left( t \right)=\pi \left( -\sin t \right)$
Hence we have, \[g'(t)=-\pi \sin t\]

pie is an irrational number. It is used in different chapters of maths such as mensuration, statistics , functions and graphs , angles and measurement.
In construction of pie charts- to find out allocations of different data is used.
In geometry pie = 180 degrees angle wise.

Note: The derivative of a function \[y=f(x)\] of a variable \[x\] is a measure of the rate at which the value of \[y\] of the function changes with respect to the change of the variable \[x\].
It is called the derivative of \[f\] with respect to \[x\] furthermore.

There are some important basic rules of differentiation that we have to always keep in mind while differentiating any function. Which are as follows:
• The constant rule or Multiplication by constant: $\left( af \right)'=af'$
• The sum rule: $\left( f+g \right)'=f'+g'$
• The subtraction rule: $\left( f-g \right)'=f'-g'$
• Fraction rule or quotient rule: \[{{\left( \dfrac{f}{g} \right)}^{'}}=\dfrac{f'g-g'f}{{{g}^{2}}}\Rightarrow \].