Solve (x)^(3)+3(x)^(2)+3x+7 | 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

$${ x }^{ 3 } +3 { x }^{ 2 } +3x+7$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

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 $nax^{n-1}$.

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

Subtract $1$ from $3$.

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

Multiply $2$ times $3$.

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

Subtract $1$ from $2$.

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

Subtract $1$ from $1$.

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

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

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

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

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

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

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

Evaluate

$x^{3}+3x^{2}+3x+7$