Solve 5x^3y-x+2-x^2+4x+10

$$5 x ^ { 3 } y - x + 2 - x ^ { 2 } + 4 x + 10$$

Differentiate w.r.t. x

$$3+15yx^{2}-2x$$

Steps Using Derivative Rule for Sum

Combine -x and 4x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}y+3x+2-x^{2}+10)$$

Add 2 and 10 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}y+3x+12-x^{2})$$

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}.

$$3\times 5yx^{3-1}+3x^{1-1}+2\left(-1\right)x^{2-1}$$

Multiply 3 times 5y.

$$15yx^{3-1}+3x^{1-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 3.

$$15yx^{2}+3x^{1-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 1.

$$15yx^{2}+3x^{0}+2\left(-1\right)x^{2-1}$$

Multiply 1 times 3.

$$15yx^{2}+3x^{0}-2x^{2-1}$$

Subtract 1 from 2.

$$15yx^{2}+3x^{0}-2x^{1}$$

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

$$15yx^{2}+3x^{0}-2x$$

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

$$15yx^{2}+3\times 1-2x$$

For any term t, t\times 1=t and 1t=t.

$$15yx^{2}+3-2x$$

Evaluate

$$12+5yx^{3}+3x-x^{2}$$