Solve (x)^(3)+3(x)^(2)+3x+1-(x)^(3)-3(x)^(2)+3x-1 | 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

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

Evaluate

$6x$

Solution Steps

Combine $x^{3}$ and $-x^{3}$ to get $0$.

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

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

$$3x+1+3x-1$$

Combine $3x$ and $3x$ to get $6x$.

$$6x+1-1$$

Subtract $1$ from $1$ to get $0$.

$$6x$$

Differentiate w.r.t. x

$6$

Steps Using Definition of a Derivative

Combine $x^{3}$ and $-x^{3}$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+3x+1-3x^{2}+3x-1)$$

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+1+3x-1)$$

Combine $3x$ and $3x$ to get $6x$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x+1-1)$$

Subtract $1$ from $1$ to get $0$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x)$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$6x^{1-1}$$

Subtract $1$ from $1$.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$