Question

Derivative of y=π5+54x+sin(2x):
Find dxdy for the function y=π5+54x+sin(2x).

Answer 1

The derivative of y=π5+54x+sin(2x) with respect to x is 54+2cos(2x). The question incorrectly asks for dxdy, but dy/dx is what is typically computed. dxdy would require the inverse function, which is not provided in the question.

Step-by-step explanation:

The question asks for dxdy for the function y=π5+54x+sin(2x). However, we usually find dy/dx, not dxdy. The correct derivative of y with respect to x is given by the derivative of each term individually:

• The constant π and the term 5 do not depend on x, so their derivative is 0.
• The derivative of 54x is simply 54.
• The derivative of sin(2x) is 2cos(2x), applying the chain rule.

So, the derivative dy/dx of the function y=π5+54x+sin(2x) is 54 + 2cos(2x). To find dxdy, which is the reciprocal of dy/dx, we would need to compute the inverse function, which might not always be possible or simple.