Solve Divide x ^ 3 + 3x ^ 2 - 2x - 5 by 3c - 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

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

Differentiate w.r.t. x

$3x^{2}+6x-7$

Steps Using Derivative Rule for Sum

Combine $-2x$ and $-5x$ to get $-7x$.

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

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 $nax^{n-1}$.

$$3x^{3-1}+2\times 3x^{2-1}-7x^{1-1}$$

Subtract $1$ from $3$.

$$3x^{2}+2\times 3x^{2-1}-7x^{1-1}$$

Multiply $2$ times $3$.

$$3x^{2}+6x^{2-1}-7x^{1-1}$$

Subtract $1$ from $2$.

$$3x^{2}+6x^{1}-7x^{1-1}$$

Subtract $1$ from $1$.

$$3x^{2}+6x^{1}-7x^{0}$$

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

$$3x^{2}+6x-7x^{0}$$

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

$$3x^{2}+6x-7$$

Evaluate

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