Solve -9x^4-16y3x^2-1

$$- 9 x ^ { 4 } - 16 y 3 x ^ { 2 } - 1$$

Differentiate w.r.t. x

$$-36x^{3}-32xy_{3}$$

Steps Using Derivative Rule for Sum

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}.

$$4\left(-9\right)x^{4-1}+2\left(-16y_{3}\right)x^{2-1}$$

Multiply 4 times -9.

$$-36x^{4-1}+2\left(-16y_{3}\right)x^{2-1}$$

Subtract 1 from 4.

$$-36x^{3}+2\left(-16y_{3}\right)x^{2-1}$$

Multiply 2 times -16y_{3}.

$$-36x^{3}+\left(-32y_{3}\right)x^{2-1}$$

Subtract 1 from 2.

$$-36x^{3}+\left(-32y_{3}\right)x^{1}$$

For any term t, t^{1}=t.

$$-36x^{3}+\left(-32y_{3}\right)x$$

Evaluate

$$-9x^{4}-16y_{3}x^{2}-1$$