Solve P(x) = x ^ 3 - 8x ^ 2 + 7x - 3 | 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

$$P(x)=x^{3}-8x^{2}+7x-3$$

Differentiate w.r.t. x

$3x^{2}-16x+7$

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 $nax^{n-1}$.

$$3x^{3-1}+2\left(-8\right)x^{2-1}+7x^{1-1}$$

Subtract $1$ from $3$.

$$3x^{2}+2\left(-8\right)x^{2-1}+7x^{1-1}$$

Multiply $2$ times $-8$.

$$3x^{2}-16x^{2-1}+7x^{1-1}$$

Subtract $1$ from $2$.

$$3x^{2}-16x^{1}+7x^{1-1}$$

Subtract $1$ from $1$.

$$3x^{2}-16x^{1}+7x^{0}$$

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

$$3x^{2}-16x+7x^{0}$$

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

$$3x^{2}-16x+7\times 1$$

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

$$3x^{2}-16x+7$$

Evaluate

$x^{3}-8x^{2}+7x-3$