y = 5x
y' = 5xln5 = ln5(5x)
y" = ln5(5xln5) = (ln5)25x = 2.59(5x)
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You can take out any constant from a derivative. In other words, this is the same as 5 times the derivative of sec x.
f(x)=(pi2)x=pi2x. The derivative of kx=ln(k)*kx, so f'(x)=2ln(pi)*pi2x (with chain rule).
I'm not sure what you're asking. The derivative of 6x is 6. The derivative of x^6 is 6x^5.
The idea is to use the chain rule. Look up the derivative of sec x, and just replace "x" with "5x". Then multiply that with the derivative of 5x.
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x