Solve 3x^3-1x^2(-2x)

$$3 x ^ { 3 } - 1 x ^ { 2 } ( - 2 x )$$

Evaluate

$$5x^{3}$$

Solution Steps

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

$$3x^{3}-1x^{3}\left(-2\right)$$

Multiply 1 and -2 to get -2.

$$3x^{3}-\left(-2x^{3}\right)$$

The opposite of -2x^{3} is 2x^{3}.

$$3x^{3}+2x^{3}$$

Combine 3x^{3} and 2x^{3} to get 5x^{3}.

$$5x^{3}$$

Differentiate w.r.t. x

$$15x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-1x^{3}\left(-2\right))$$

Multiply 1 and -2 to get -2.

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

The opposite of -2x^{3} is 2x^{3}.

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

Combine 3x^{3} and 2x^{3} to get 5x^{3}.

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

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

$$3\times 5x^{3-1}$$

Multiply 3 times 5.

$$15x^{3-1}$$

Subtract 1 from 3.

$$15x^{2}$$