Derivatives Find and simplify the derivative of the following ...

Question

Derivatives Find and simplify the derivative of the following functions.

f(x) = 3x⁴(2x²−1)

Accepted Answer

Welcome back, everyone. Determine the derivative of the function H of Y equals 2 the power of 5th multiplied by Y2 + 2 and were given for answer choices. A says that H of Y equals 10 the power of 6 plus 4 the power of fifth plus 20s the power of 4th. B says that H of Y equals 14 the power of 6 plus 20s the power of 4th. C says that H of Y equals 10 the power of 6 plus 20s the power of 4th and D says that H of Y equals 14 the power of 6 plus 4 the power of fifth plus 2y. What we want to do is simply evaluate the derivative of the given function. We can notice that it is a product of two functions, so we can apply the power rule. But whenever we want to apply a specific rule, we first of all want to check if this function. Can be simplified. We can first of all distribute the terms and avoid the power rule because, well, applying the power rule is more complex. It takes more time. We need to find more derivatives. So what we're going to do instead is distribute the terms. We have 25th multiplied by Y2 which gives us 2 the power of 7th. And then we multiply 2 whites the power of fifth by 2, which gives us 4 whites the power of fifth. And now we can differentiate this by applying the power rule only, which is much easier. So we take 2 multiplied by whites the power of 7th derivative. Plus 4 multiplied by white it's the power of fifth derivative. Here we are applying the power, the power rule for each term, and we get 2 multiplied by. We bring down the 7 and the original exponent decreases by 1 unit. So we take y to the power of 7 minus 1. And then we add 4 multiplied by we bring down the exponent, which gives us 5 y to the power of 5 minus 1 and overall we get 14 y to the power of 6 plus 20 y to the power of 4th. And that's how we have evaluated the derivative. Now, if we consider the answer choices, we can notice that B is the correct answer to this problem. Thank you for watching.

Derivatives Find and simplify the derivative of the following functions.
f(x) = 3x⁴(2x²−1)

Key Concepts

Derivatives

Product Rule

Simplification of Derivatives

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