How do you calculate the derivative for #y = 3(5 - x^2)^5#?

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Answer 1 · 2015-08-01T18:13:52

#y^' = -30x * (5-x^2)^4#

You can differentiate your function, whichcan be written as

#y = 3u^5#, with #u = 5-x^2#

by using the chain rule

#color(blue)(d/dx(y) = d/(du)(y) * d/dx(u))#

In your case, the derivative of #y# would be

#d/dx(3u^5) = d/(du)(3u^5) * d/dx(5-x^2)#

#d/dx(3u^5) = 15u^4 * (-2x)#

#d/dx(3(5-x^2)^5) = 15(5-x^2)^4 * (-2x)#

This is equivalent to

#y^' = color(green)(-30x * (5-x^2)^4)#