Higher-order derivatives Find and simplify y''.
y = 2^x ...

Question

Higher-order derivatives Find and simplify y''.

y = 2^x x

Accepted Answer

Calculate the second derivative of the function Y equals 5 X X2. Where we have 4 possible answers, variations of 5 to the X, multiplied by another expression. Now, to solve this, we first need to find the first derivative using the product rule. The private rule tells us. That if we have two functions multiplying each other, F and G The derivative is equivalent to F multiplied by G. Plus F multiplied by G. So in our first derivative, We have 5 Ra CDX multiplied by X squared. Or F will be 5 to the X, G will be X squared. F then will be 5 X. Natural log of 5. This is using the derivative of the base exponential function. DD X B X equals BX natural log of B. For G, we are making use of the power rule. G will just be 2 X. Our product rule for the first derivative then. Will be F, which is 5 X, natural log of 5. Multiplied by G is X2. Plus F fiber the X multiplied by G or 2 X. Now, we will apply the product rule again to find the second derivative. So, we have 2 different product rules here to do. Actually going to rearrange this first, cause we get 5 to the X X squared multiplied by natural log of 5. Plus 2 X multiplied by 5, race to the X. Now, we can find a derivative. We notice we have 5 to the X X squared again. Which we actually just took that derivative. So, for the second derivative. We get 5 to the X. Natural log of 5 multiplied by X2. Plus 5 the X 2 X. All multiplied by the natural log of 5. Naturallog 5 is a constant, so it will stay in the front. Now we look at our derivative to X 5 X. This one is another product tool. Where F equals to X. G equals 5 ver the X. F prime will be 2. G will be 5 rates the X, natural log of 5. So then, we can add our next products. 2 multiplied. By 5 Ray City X. Plus 2 X multiplied by 5 is the X, natural log of 5. From here we can simplify our equation. Let's multiply out our natural log of 5. We get 5 rates to the X X squared. Natural log of 5 squared. Plus 5 for the X. 2 X natural log 5. Plus 2, raise the 5 X. Plus 2 X 5 versus the X. Natural law of 5. We noticed there's a 5 to the X on every term, so we can factor this out. 5 to the X. X squared, natural log 5 squared. Plus 2 X, natural log of 5. Plus 2 Plus 2 x nalog 5. Finally, we can combine. Our 2 X natural log 5s, to get 5 X multiplied by X2, natural log squared 5. Plus 4 X natural log of 5. Plus 2 We can't simplify this problem anymore. So, if you look at our possible answers, We can determine the answer to our problem. Is answer D. OK. I hope that help you solve the problem. Thank you for watching. Goodbye.

Higher-order derivatives Find and simplify y''.y = 2^x x

Watch next

Higher-order derivatives Find and simplify y''.
y = 2^x x