Solve 5x/2*8x^2/10

$$\frac { 5 x } { 2 } \times \frac { 8 x ^ { 2 } } { 10 }$$

Evaluate

$$2x^{3}$$

Solution Steps

Divide 8x^{2} by 10 to get \frac{4}{5}x^{2}.

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

Multiply \frac{5x}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2\times 5 in both numerator and denominator.

$$2xx^{2}$$

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

$$2x^{3}$$

Differentiate w.r.t. x

$$6x^{2}$$

Steps Using Definition of a Derivative

Divide 8x^{2} by 10 to get \frac{4}{5}x^{2}.

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

Multiply \frac{5x}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2xx^{2})$$

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

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

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

$$3\times 2x^{3-1}$$

Multiply 3 times 2.

$$6x^{3-1}$$

Subtract 1 from 3.

$$6x^{2}$$