Solve 5x^3*2x=

$$5 x ^ { 3 } \times 2 x =$$

Evaluate

$$10x^{4}$$

Solution Steps

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

$$5x^{4}\times 2$$

Multiply 5 and 2 to get 10.

$$10x^{4}$$

Differentiate w.r.t. x

$$40x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{4}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{4})$$

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

$$4\times 10x^{4-1}$$

Multiply 4 times 10.

$$40x^{4-1}$$

Subtract 1 from 4.

$$40x^{3}$$