Solve 4x^2*6x^3=

$$4 x ^ { 2 } \cdot 6 x ^ { 3 } =$$

Evaluate

$$24x^{5}$$

Solution Steps

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

$$4x^{5}\times 6$$

Multiply 4 and 6 to get 24.

$$24x^{5}$$

Differentiate w.r.t. x

$$120x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{5}\times 6)$$

Multiply 4 and 6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{5})$$

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

$$5\times 24x^{5-1}$$

Multiply 5 times 24.

$$120x^{5-1}$$

Subtract 1 from 5.

$$120x^{4}$$