Solve f(x)=x^3-1yg(x)2x^3-1

$$f ( x ) = x ^ { 3 } - 1 y g ( x ) 2 x ^ { 3 } - 1$$

Differentiate w.r.t. x

$$x^{2}\left(3-8gxy\right)$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-1ygx^{4}\times 2-1)$$

Multiply 1 and 2 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-2ygx^{4}-1)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3x^{3-1}+4\left(-2gy\right)x^{4-1}$$

Subtract 1 from 3.

$$3x^{2}+4\left(-2gy\right)x^{4-1}$$

Multiply 4 times -2yg.

$$3x^{2}+\left(-8gy\right)x^{4-1}$$

Subtract 1 from 4.

$$3x^{2}+\left(-8gy\right)x^{3}$$

Evaluate

$$x^{3}-2gyx^{4}-1$$