Solve 1div2(4x*9x^3)

$$1 \div 2(4x \times 9 { x }^{ 3 } )$$

Evaluate

$$18x^{4}$$

Solution Steps

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

$$\frac{1}{2}\times 4x^{4}\times 9$$

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

$$2x^{4}\times 9$$

Multiply 2 and 9 to get 18.

$$18x^{4}$$

Differentiate w.r.t. x

$$72x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\times 4x^{4}\times 9)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 9)$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{4})$$

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

$$4\times 18x^{4-1}$$

Multiply 4 times 18.

$$72x^{4-1}$$

Subtract 1 from 4.

$$72x^{3}$$