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What is the derivative of 3x ?

Answer
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Hint: In this question , we need to find the derivative of 3x. Mathematically, derivative is nothing but a rate of change of function with respect to an independent variable given in the function. Differentiation is used to calculate the derivatives. In two ways we can find the derivative of 3x. We can find the derivative by taking logs on both sides. Also there is a direct formula to find the derivative of 3x .
Logarithmic rule used :
log mn=nlog m
Derivative formula used :
1.ddx (logx)=1x
2. ddx (x)=1

Complete step-by-step solution:
Given ,
3x
Let us consider , y=3x
On taking log on both sides,
We get,
log y=log(3x)
We know that log mn=nlog m
By using that logarithmic rule,
We get,
log y=x log 3
On differentiating y with respect to x,
We get ,
dydx(log y)=dydx(x log 3)
1ydydx=1×(log 3)
By cross multiplying,
We get,
dydx=y(log 3)
We have already considered y=3x,
By substituting the value of y,
We get,
dydx=3x(log 3)
Thus we get the derivative of 3x  is 3x(log 3)
Final answer :
The derivative of 3x is 3x(log 3)

Note: Derivative helps in solving the problems in calculus and in differential equations. The derivative of y with respect to x is represented as dydx. There are two types of derivative namely first order derivative and second order derivative. A simple example for a derivative is the derivative of x3 is 3x . Derivative is also applicable in trigonometric functions.
Alternative solution :
We can also find the derivative of 3x by using a derivative formula.
Formula used :
ddx(ax)= axloga
Given,
3x
Here a=3
By substituting the value of a in the formula,
We get,
ddx(3x)= 3xlog3
Thus we get the derivative of 3x is 3x(log 3)