Solve 3/4x^5*2/3x^3=

$$\frac { 3 } { 4 } x ^ { 5 } \cdot \frac { 2 } { 3 } x ^ { 3 } =$$

Evaluate

$$\frac{x^{8}}{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{3}{4}x^{8}\times \frac{2}{3}$$

Multiply \frac{3}{4} and \frac{2}{3} to get \frac{1}{2}.

$$\frac{1}{2}x^{8}$$

Differentiate w.r.t. x

$$4x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x^{8}\times \frac{2}{3})$$

Multiply \frac{3}{4} and \frac{2}{3} to get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8\times \frac{1}{2}x^{8-1}$$

Multiply 8 times \frac{1}{2}.

$$4x^{8-1}$$

Subtract 1 from 8.

$$4x^{7}$$