. Find 𝑓′(𝑥) and simplify. = 5𝑥^−3(2𝑥^5 − 3𝑥^3 − 4)

Question

Find 𝑓′(𝑥) and simplify. =

5𝑥^−3(2𝑥^5 − 3𝑥^3 − 4)

𝑓(𝑥) = csc 𝑥 /(𝑥^3+5)

Answer 1

If you really mean that the whole parenthesis beginning with -3 is the exponent:

then f'(x) = 5{-3(2x⁵-3x³-4)[-3(10x⁴ - 9x²)]x^[-3(2x⁵ - 3x³-4)-1].

For the second one I will tell you a mnemonic I learned recently:

downsie d upsie - upsie d downsie divided by downsie squeared