Find the Derivative - d/d@VAR f(x)=x^4-54x^2+13

Problem

d()/d(x)*(x4−54*x2+13)

Solution

1. Identify the function ƒ(x)=x4−54*x2+13 and apply the sum rule for derivatives, which allows for differentiating each term individually.

2. Apply the power rule to the first term x4 The power rule states that d(xn)/d(x)=n*x(n−1)

d(x4)/d(x)=4*x3

3. Apply the power rule to the second term −54*x2 Multiply the exponent by the coefficient and decrease the exponent by one.

(d(−)*54*x2)/d(x)=−108*x

4. Apply the constant rule to the third term 13 The derivative of any constant is zero.

d(13)/d(x)=0

5. Combine the results of the individual derivatives to find the final expression for ƒ(x)′

ƒ(x)′=4*x3−108*x

Final Answer

d()/d(x)*(x4−54*x2+13)=4*x3−108*x

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