Find the derivative dy/dx of the function f(x) = 5x^4 - 3x^2 + 7x - 12.
Answer and explanation
Correct answer: C. 20x^3 - 6x + 7
- Step 1: Apply the power rule d/dx [x^n] = n*x^(n-1) to each polynomial term individually.
- Step 2: d/dx [5x^4] = 20x^3, d/dx [-3x^2] = -6x, d/dx [7x] = 7, and d/dx [-12] = 0, giving 20x^3 - 6x + 7.
Answer
20x^3 - 6x + 7.
Why not the others: '20x^3 - 6x' incorrectly omits the linear coefficient derivative of 7x; '5x^3 - 6x + 7' fails to multiply 5 by the exponent 4; '20x^4 - 6x^2 + 7' fails to decrement exponents.
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