Solve x ^ 3 - 5x ^ 2 + x + 2 + x ^ 3 - 3x ^ 2 + 2x + 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

$2x^{3}-8x^{2}+3x+4$

Solution Steps

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

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

Combine $-5x^{2}$ and $-3x^{2}$ to get $-8x^{2}$.

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

Combine $x$ and $2x$ to get $3x$.

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

Add $2$ and $2$ to get $4$.

$$2x^{3}-8x^{2}+3x+4$$

Differentiate w.r.t. x

$6x^{2}-16x+3$

Steps Using Derivative Rule for Sum

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

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

Combine $-5x^{2}$ and $-3x^{2}$ to get $-8x^{2}$.

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

Combine $x$ and $2x$ to get $3x$.

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

Add $2$ and $2$ to get $4$.

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

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 $nax^{n-1}$.

$$3\times 2x^{3-1}+2\left(-8\right)x^{2-1}+3x^{1-1}$$

Multiply $3$ times $2$.

$$6x^{3-1}+2\left(-8\right)x^{2-1}+3x^{1-1}$$

Subtract $1$ from $3$.

$$6x^{2}+2\left(-8\right)x^{2-1}+3x^{1-1}$$

Multiply $2$ times $-8$.

$$6x^{2}-16x^{2-1}+3x^{1-1}$$

Subtract $1$ from $2$.

$$6x^{2}-16x^{1}+3x^{1-1}$$

Subtract $1$ from $1$.

$$6x^{2}-16x^{1}+3x^{0}$$

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

$$6x^{2}-16x+3x^{0}$$

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

$$6x^{2}-16x+3\times 1$$

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

$$6x^{2}-16x+3$$