f(x) = square root of 7x + x2

Question

Calculate the derivative of the function.

 

Square root of 7x plus x to the second power

Answer 1

Hi Jordan,

 

First note that square root means to the power one half or 1/2. So let's rewrite f(x) as:

 

f(x) = [7x+(x²)]^1/2

 

Now, the important thing to remember is that whenever you see there is a power, you should use the power rule first. 

 

Power rule says that the power would come down and become the coefficient, and then the new power would be the old power minus one. After we do that, we should multiply the whole thing by the derivative of the inside as part of the chain rule.

 

 

so f'(x) = (1/2)*[7x+(x²)]^-1/2 * [7+2x]

 

explanation: as mentioned previously, the power (1/2) became the coefficient, new power became -1/2 since (0.5-1=-0.5) and finally the derivative of the term inside the bracket is 7 + 2x which should be multiplied by the whole thing. 

 

We are done, but you could rewrite another way by taking the term involving negative power down (in the denominator) and changing the sign of power from negative to positive.

 

 

 

                                     0.5* (7+2x)

so we can write:  f'(x) = -----------------         where sqrt stands for square root (power 1/2)

                                     sqrt (7x+x²)