Find the Derivative - d/d@VAR f(x)=x^5-3x^4

Problem

d()/d(x)*(x5−3*x4)

Solution

1. Identify the function to be differentiated, which is a polynomial consisting of two terms: x5 and −3*x4

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(x5−3*x4)=d(x5)/d(x)−(d(3)*x4)/d(x)

3. Apply the power rule to the first term, x5 The power rule states that d(xn)/d(x)=n*x(n−1)

d(x5)/d(x)=5*x4

4. Apply the constant multiple rule and the power rule to the second term, 3*x4

(d(3)*x4)/d(x)=3⋅4*x3

5. Simplify the expression by performing the multiplication.

3⋅4*x3=12*x3

6. Combine the results to find the final derivative.

5*x4−12*x3

Final Answer

d()/d(x)*(x5−3*x4)=5*x4−12*x3

Want more problems? Check here!