Solve 2/5x^2*25x

$$\frac { 2 } { 5 } x ^ { 2 } \times 25 x$$

Evaluate

$$10x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{2}{5}x^{3}\times 25$$

Multiply \frac{2}{5} and 25 to get 10.

$$10x^{3}$$

Differentiate w.r.t. x

$$30x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{5}x^{3}\times 25)$$

Multiply \frac{2}{5} and 25 to get 10.

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

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

$$3\times 10x^{3-1}$$

Multiply 3 times 10.

$$30x^{3-1}$$

Subtract 1 from 3.

$$30x^{2}$$