Solve x ^ 3 + p * x ^ 2 + 9x + 5; 2(x) | 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

$$x^{3}+px^{2}+9x+5; 2(x)$$

Differentiate w.r.t. x

$3x^{2}+2px+q$

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 $nax^{n-1}$.

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

Subtract $1$ from $3$.

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

Subtract $1$ from $2$.

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

Subtract $1$ from $1$.

$$3x^{2}+2px^{1}+qx^{0}$$

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

$$3x^{2}+2px+qx^{0}$$

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

$$3x^{2}+2px+q\times 1$$

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

$$3x^{2}+2px+q$$

Evaluate

$x^{3}+px^{2}+qx+5$