Solve 6x^5*3x^5*x^0

$$6 x ^ { 5 } \cdot 3 x ^ { 5 } \cdot x ^ { 0 }$$

Evaluate

$$18x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$6x^{10}\times 3x^{0}$$

To multiply powers of the same base, add their exponents. Add 10 and 0 to get 10.

$$6x^{10}\times 3$$

Multiply 6 and 3 to get 18.

$$18x^{10}$$

Differentiate w.r.t. x

$$180x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{10}\times 3x^{0})$$

To multiply powers of the same base, add their exponents. Add 10 and 0 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{10}\times 3)$$

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{10})$$

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

$$10\times 18x^{10-1}$$

Multiply 10 times 18.

$$180x^{10-1}$$

Subtract 1 from 10.

$$180x^{9}$$