Question

Find the deivative of the function
y(x) = 25x^7−10x^7/5x^4

Answer 1

The derivative is,

`dy/dx = 175x^(6)-30x^(2)\\`

Explanation:

We have the function,

`y(x) = 25x^7-10x^7/(5x^4)`

Simplifying,

`y(x) = 25x^7-10x^7/(5x^4)\\\\y(x) = 25x^7-10x^3`

Now, calculating the derivative,

`d/dx[y(x)] = d/dx[25x^7-10x^3]\\dy/dx=d/dx[25x^7]-d/dx[10x^3]\\dy/dx=25d/dx[x^7]-10d/dx[x^3]\\dy/dx = 25(7)x^(7-1)-10(3)x^(3-1)\\dy/dx = 175x^(6)-30x^(2)\\`

Hence we have found the derivative