Solve {l}{10x^2-3x^3+6^2}{*4}

$$\left. \begin{array} { l } { 10 x ^ { 2 } - 3 x ^ { 3 } + 6 ^ { 2 } } \\ { \times 4 } \end{array} \right.$$

Evaluate

$$144+10x^{2}-3x^{3}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$10x^{2}-3x^{3}+36\times 4$$

Multiply 36 and 4 to get 144.

$$10x^{2}-3x^{3}+144$$

Differentiate w.r.t. x

$$x\left(20-9x\right)$$

Steps Using Derivative Rule for Sum

Calculate 6 to the power of 2 and get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}-3x^{3}+36\times 4)$$

Multiply 36 and 4 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{2}-3x^{3}+144)$$

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}.

$$2\times 10x^{2-1}+3\left(-3\right)x^{3-1}$$

Multiply 2 times 10.

$$20x^{2-1}+3\left(-3\right)x^{3-1}$$

Subtract 1 from 2.

$$20x^{1}+3\left(-3\right)x^{3-1}$$

Multiply 3 times -3.

$$20x^{1}-9x^{3-1}$$

Subtract 1 from 3.

$$20x^{1}-9x^{2}$$

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

$$20x-9x^{2}$$