Solve 625x^3-625x^4-61

$$625 { x }^{ 3 } -625 { x }^{ 4 } -61$$

Differentiate w.r.t. x

$$625\left(3-4x\right)x^{2}$$

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}.

$$3\times 625x^{3-1}+4\left(-625\right)x^{4-1}$$

Multiply 3 times 625.

$$1875x^{3-1}+4\left(-625\right)x^{4-1}$$

Subtract 1 from 3.

$$1875x^{2}+4\left(-625\right)x^{4-1}$$

Multiply 4 times -625.

$$1875x^{2}-2500x^{4-1}$$

Subtract 1 from 4.

$$1875x^{2}-2500x^{3}$$

Evaluate

$$-625x^{4}+625x^{3}-61$$