Find the Derivative - d/dx y=100/(x^4)

Problem

d()/d(x)100/(x4)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

y=100*x(−4)

2. Apply the power rule for derivatives, which states that d(xn)/d(x)=n*x(n−1)

d(y)/d(x)=100⋅(−4*x(−4−1))

3. Multiply the constants and simplify the exponent.

d(y)/d(x)=−400*x(−5)

4. Rewrite the expression with a positive exponent by moving the variable to the denominator.

d(y)/d(x)=−400/(x5)

Final Answer

d()/d(x)100/(x4)=−400/(x5)

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