Solve 6x^4*3x

$$6 x ^ { 4 } \times 3 x$$

Evaluate

$$18x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply 6 and 3 to get 18.

$$18x^{5}$$

Differentiate w.r.t. x

$$90x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{5})$$

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

$$5\times 18x^{5-1}$$

Multiply 5 times 18.

$$90x^{5-1}$$

Subtract 1 from 5.

$$90x^{4}$$