Evaluate and simplify y'.
y = 2x^√2

Question

Evaluate and simplify y'.

y = 2x^√2

Accepted Answer

Welcome back, everyone. In this problem, we want to find the derivative of the function F X equals 5 X to the power of route 7. A says the derivative is 5 route 7, X raise to the power of route 7 + 1. B 7 route 5X raised to Route 7 + 1. C 5 route 7X raised to route 7 minus 1, and D 7 route 5X raised to route 7 minus 1. Now, what do we know here? Well, notice that to differentiate F of X, OK, then we could use the power rule because we have our term X being raised to a power. What does the power rule of differentiation say? Recall that it tells us that if we have Y. If we have a function y equals x to the power of n. Then the derivative of Y with respect to X is going to be equal to N X N minus 1. In other words, we bring down the power and subtract one from the original power. So in that case for FX equals 5 x rays to the poor of route seven, then that means the derivative of FF X by the poor rule will be equal to route 7. We bring down the poor multiplied by 5 or a term that was already there, multiplied by X rates to the poor of Route 7 minus 1. We subtract 1 from the poor. Route 7 multiplied by 5, we can rewrite that as 5 route 7. So the derivative of F of X is 5 route 7 multiplied by X raised to the power of Route 7 minus 1. If we look back at our answer choices, that means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Evaluate and simplify y'.y = 2x√2

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Evaluate and simplify y'.
y = 2x^√2