Solve 5x^2-3x+1text{toget}3x^3+7x^2+8

$$5 x ^ { 2 } - 3 x + 1 \text { to get } 3 x ^ { 3 } + 7 x ^ { 2 } + 8$$

Differentiate w.r.t. x

$$24x+9ego\left(tx\right)^{2}-3$$

Steps Using Derivative Rule for Sum

Multiply t and t to get t^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-3x+1t^{2}oge\times 3x^{3}+7x^{2}+8)$$

Multiply 1 and 3 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-3x+3t^{2}ogex^{3}+7x^{2}+8)$$

Combine 5x^{2} and 7x^{2} to get 12x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}-3x+3t^{2}ogex^{3}+8)$$

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}.

$$2\times 12x^{2-1}-3x^{1-1}+3\times 3egot^{2}x^{3-1}$$

Multiply 2 times 12.

$$24x^{2-1}-3x^{1-1}+3\times 3egot^{2}x^{3-1}$$

Subtract 1 from 2.

$$24x^{1}-3x^{1-1}+3\times 3egot^{2}x^{3-1}$$

Subtract 1 from 1.

$$24x^{1}-3x^{0}+3\times 3egot^{2}x^{3-1}$$

Multiply 1 times -3.

$$24x^{1}-3x^{0}+9egot^{2}x^{3-1}$$

Subtract 1 from 3.

$$24x^{1}-3x^{0}+9egot^{2}x^{2}$$

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

$$24x-3x^{0}+9egot^{2}x^{2}$$

For any term t except 0, t^{0}=1.

$$24x-3+9egot^{2}x^{2}$$

Evaluate

$$3egot^{2}x^{3}+12x^{2}-3x+8$$