Find the Derivative - d/d@VAR f(x)=1/(x^4)

Problem

d()/d(x)1/(x4)

Solution

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

1/(x4)=x(−4)

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

d(x(−4))/d(x)=−4*x(−4−1)

3. Simplify the exponent by performing the subtraction.

−4*x(−4−1)=−4*x(−5)

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

−4*x(−5)=−4/(x5)

Final Answer

d()/d(x)1/(x4)=−4/(x5)

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