Find dy/dx sin(y)=5x^4-5

Problem

sin(y)=5*x4−5

Solution

1. Differentiate both sides with respect to x using the chain rule for the term involving y

d(sin(y))/d(x)=d(5*x4−5)/d(x)

2. Apply the chain rule to the left side, noting that the derivative of sin(y) is cos(y)d(y)/d(x)

cos(y)d(y)/d(x)=20*x3

3. Isolate the derivative d(y)/d(x) by dividing both sides of the equation by cos(y)

d(y)/d(x)=(20*x3)/cos(y)

Final Answer

d(y)/d(x)=(20*x3)/cos(y)

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