Why does the derivative of e^5x = 5e^5 instead of e^5x
Also does dy/dx and d/dx mean the same thing?
#Derivative of e^5x
ember lava
tender lynxBOT
Why does the derivative of e^5x = 5e^5 instead of e^5x
Also does dy/dx and d/dx...
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wet viper
Why does the derivative of e^5x = 5e^5 instead of e^5x
Also does dy/dx and d/dx...
are you familiar with the chain rule?
ember lava
are you familiar with the chain rule?
Yes but why would the chain rule apply
wet viper
Yes but why would the chain rule apply
you're composing the functions e^x and 5x
so in the chain rule f(x) is e^x and u(x) is 5x
ember lava
Ah thanks but what about dy/dx? I know it means derivative in respect to x but i never understood what that meant
wet viper
Ah thanks but what about dy/dx? I know it means derivative in respect to x but i...
it means the rate of change of y with respect to x (which is just the derivative, yeah). it comes from the limit definition of the derivate. to calculate the gradient of a straight line you'd do Δy/Δx, and in the definition of a derivative you basically do this but for really small changes, hence the Δ's become d's
hoary moonBOT
@ember lava
quick knoll
Ah thanks but what about dy/dx? I know it means derivative in respect to x but i...
you know that d/dx is "differentiating something with respect to x"
and so, when you put a y (dy/dx) that's differentiating y with respect to x
so if you have y = 3x^2 + 2x +1 and a = 4x^6 +2
dy/dx = 6x +2
da/dx = 24x^5
the little letter next to the d just means the function you're differentiating