Solve (3x*5x^2)-(x^2*2x)

$$( 3 x \times 5 x ^ { 2 } ) - ( x ^ { 2 } \times 2 x )$$

Evaluate

$$13x^{3}$$

Solution Steps

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

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

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

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

Multiply 3 and 5 to get 15.

$$15x^{3}-x^{3}\times 2$$

Combine 15x^{3} and -x^{3}\times 2 to get 13x^{3}.

$$13x^{3}$$

Differentiate w.r.t. x

$$39x^{2}$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{3}-x^{3}\times 2)$$

Combine 15x^{3} and -x^{3}\times 2 to get 13x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13x^{3})$$

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

$$3\times 13x^{3-1}$$

Multiply 3 times 13.

$$39x^{3-1}$$

Subtract 1 from 3.

$$39x^{2}$$