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To differentiate a function with respect to (wrt) x you multiply the function by the power and then lower the power by one. For example, if f(x)=x^3, then to differentiate you multiply the function by 3 (...

As we are told the number of girls that are in the school, our first step should be to calculate the number of boys in the school through a simple subtraction (1200-575 = 625). After this we are told that...

X+2/5X = 63 or 63 = 140%

First we need to understand that the original price (X) has been increased by 40%. Hence, by 2/5 (40/100 = 40%) of its original value, in other words, 2/5X.

To find ...

So this function is the product of two functions of x, so we use the product rule to differentiate it. The rule states if y=uv, dy/dx=(du/dx)v+(dv/dx)u. In this function we assign u=(4x+1)³ and...

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y²/2 = -x...