Question

Find dy/dx.. y=3x^4-x^2+1

Answer 1

Dy/dx=y'(x)=12x³-2x 
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Answer 2

To find dy/dx (the derivative of y with respect to x) of the given function y = 3x^4 - x^2 + 1, we need to differentiate each term with respect to x using the power rule of differentiation. The power rule states that if we have a term of the form ax^n, its derivative with respect to x is nax^(n-1).

Let's find the derivative step by step:

1. Differentiate the term 3x^4: d/dx (3x^4) = 4 * 3x^(4-1) = 12x^3

2. Differentiate the term -x^2: d/dx (-x^2) = 2 * (-1) * x^(2-1) = -2x

3. The derivative of a constant (1 in this case) is zero: d/dx (1) = 0

Now, sum up the derivatives of each term to find dy/dx:

dy/dx = 12x^3 - 2x + 0

So, the derivative of the function y = 3x^4 - x^2 + 1 with respect to x is dy/dx = 12x^3 - 2x.