Find the Derivative - d/dx 5/(x^4)

Problem

d()/d(x)5/(x4)

Solution

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

5/(x4)=5*x(−4)

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

(d(5)*x(−4))/d(x)=5⋅(−4)*x(−4−1)

3. Simplify the coefficient and the exponent.

5⋅(−4)*x(−5)=−20*x(−5)

4. Convert the expression back into a fraction by moving the variable with the negative exponent to the denominator.

−20*x(−5)=−20/(x5)

Final Answer

d()/d(x)5/(x4)=−20/(x5)

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