How are the derivatives of sin^−1 x and cos^−1 x related?

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Accepted Answer

Select the correct relationship between the derivative of F of X and G of X. Where we have F of X equals sine inverse of 5 X and G of X equals cosine inverse of 5 X. We also have 4 possible answers, being F equals 5 multiplied by G. F equals -5 multiplied by G. F equals negative G and F equals G. Now, to solve this, let's first find our derivatives. The derivative Of the inverse sign function. Is given by one divided by the square root. Of 1 minus X2. Now, if we apply this to our function for F, We will say we have 1 divided by the square root of 1 minus 5 x 2. Now, this derivative is actually a chain rule derivative, which means we also multiply by the derivative of the inside function. Which is just 5. Now, we will do the same for cosine. And verse Now, for cosine inverse, the derivative is -1 divided by the square root of 1 minus X2. So similar to the previous derivative, we will say 1 divided by the square root of 1 minus 5 x squared. Multiplied by the inside derivative of 5, and this one is negative. We can now simplify this. Ticket 5. Divided by Square root of 1 minus 25 x squared. And for our G prime. -5 divided by the square root of 1 minus 25 X2. So, we have F, and now we also have G. We can then see F and G are the same except for the negative being in front of the G. We can then confirm. That F of X is the same derivative as G of X, but negative. This means the answer to our problem is answer C. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

How are the derivatives of sin^−1 x and cos^−1 x related?

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