Solve 13--5mx^3+4x^2-mx^3+8

$$13--5m { x }^{ 3 } +4 { x }^{ 2 } -m { x }^{ 3 } +8$$

Differentiate w.r.t. x

$$4x\left(3mx+2\right)$$

Steps Using Derivative Rule for Sum

The opposite of -5mx^{3} is 5mx^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13+5mx^{3}+4x^{2}-mx^{3}+8)$$

Combine 5mx^{3} and -mx^{3} to get 4mx^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(13+4mx^{3}+4x^{2}+8)$$

Add 13 and 8 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(21+4mx^{3}+4x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 4x^{2-1}+3\times 4mx^{3-1}$$

Multiply 2 times 4.

$$8x^{2-1}+3\times 4mx^{3-1}$$

Subtract 1 from 2.

$$8x^{1}+3\times 4mx^{3-1}$$

Multiply 3 times 4m.

$$8x^{1}+12mx^{3-1}$$

Subtract 1 from 3.

$$8x^{1}+12mx^{2}$$

For any term t, t^{1}=t.

$$8x+12mx^{2}$$

Evaluate

$$4mx^{3}+4x^{2}+21$$