Solve 5x^2*3x^8

$$5 x ^ { 2 } \cdot 3 x ^ { 8 }$$

Evaluate

$$15x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$5x^{10}\times 3$$

Multiply 5 and 3 to get 15.

$$15x^{10}$$

Differentiate w.r.t. x

$$150x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{10}\times 3)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{10})$$

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

$$10\times 15x^{10-1}$$

Multiply 10 times 15.

$$150x^{10-1}$$

Subtract 1 from 10.

$$150x^{9}$$