Solve 3/2x^3*6x^2

$$\frac{ 3 }{ 2 } { x }^{ 3 } \times 6 { x }^{ 2 }$$

Evaluate

$$9x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{3}{2}x^{5}\times 6$$

Multiply \frac{3}{2} and 6 to get 9.

$$9x^{5}$$

Differentiate w.r.t. x

$$45x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2}x^{5}\times 6)$$

Multiply \frac{3}{2} and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{5})$$

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

$$5\times 9x^{5-1}$$

Multiply 5 times 9.

$$45x^{5-1}$$

Subtract 1 from 5.

$$45x^{4}$$