Solve -270x^4+216x^3-54x^24x

$$-270 { x }^{ 4 } +216 { x }^{ 3 } -54 { x }^{ 2 } 4x$$

Evaluate

$$-270x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-270x^{4}+216x^{3}-54x^{3}\times 4$$

Multiply 54 and 4 to get 216.

$$-270x^{4}+216x^{3}-216x^{3}$$

Combine 216x^{3} and -216x^{3} to get 0.

$$-270x^{4}$$

Differentiate w.r.t. x

$$-1080x^{3}$$

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}.

$$4\left(-270\right)x^{4-1}+3\times 216x^{3-1}+2\left(-216x\right)x^{2-1}$$

Multiply 4 times -270.

$$-1080x^{4-1}+3\times 216x^{3-1}+2\left(-216x\right)x^{2-1}$$

Subtract 1 from 4.

$$-1080x^{3}+3\times 216x^{3-1}+2\left(-216x\right)x^{2-1}$$

Multiply 3 times 216.

$$-1080x^{3}+648x^{3-1}+2\left(-216x\right)x^{2-1}$$

Subtract 1 from 3.

$$-1080x^{3}+648x^{2}+2\left(-216x\right)x^{2-1}$$

Multiply 3 times 216.

$$-1080x^{3}+648x^{2}+\left(-432x\right)x^{2-1}$$

Subtract 1 from 2.

$$-1080x^{3}+648x^{2}+\left(-432x\right)x^{1}$$

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

$$-1080x^{3}+648x^{2}+\left(-432x\right)x$$