Solve (-7/3x^3)*(-4/7x)+2/3x^4=

$$( - \frac { 7 } { 3 } x ^ { 3 } ) \cdot ( - \frac { 4 } { 7 } x ) + \frac { 2 } { 3 } x ^ { 4 } =$$

Evaluate

$$2x^{4}$$

Solution Steps

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

$$-\frac{7}{3}x^{4}\left(-\frac{4}{7}\right)+\frac{2}{3}x^{4}$$

Multiply -\frac{7}{3} and -\frac{4}{7} to get \frac{4}{3}.

$$\frac{4}{3}x^{4}+\frac{2}{3}x^{4}$$

Combine \frac{4}{3}x^{4} and \frac{2}{3}x^{4} to get 2x^{4}.

$$2x^{4}$$

Differentiate w.r.t. x

$$8x^{3}$$

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}.

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

Multiply 3 times -\frac{7}{3}\left(-\frac{4}{7}\right)x.

$$4xx^{3-1}+4\times \frac{2}{3}x^{4-1}$$

Subtract 1 from 3.

$$4xx^{2}+4\times \frac{2}{3}x^{4-1}$$

Multiply 4 times \frac{2}{3}.

$$4xx^{2}+\frac{8}{3}x^{4-1}$$

Subtract 1 from 4.

$$4xx^{2}+\frac{8}{3}x^{3}$$