Find the Derivative - d/dx (4x^3+3x^2)/x

Problem

d()/d(x)(4*x3+3*x2)/x

Solution

1. Simplify the expression before differentiating by dividing each term in the numerator by the denominator x

(4*x3+3*x2)/x=(4*x3)/x+(3*x2)/x

2. Reduce the powers of x using the laws of exponents.

4*x2+3*x

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term of the simplified expression.

(d(4)*x2)/d(x)=8*x

(d(3)*x)/d(x)=3

4. Combine the results to find the final derivative.

8*x+3

Final Answer

d()/d(x)(4*x3+3*x2)/x=8*x+3

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