Solve f(x) = 2x ^ 3 - 5x ^ 2 + 4x + 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

$$f(x)=2x^{3}-5x^{2}+4x+1$$

Differentiate w.r.t. x

$2\left(x-1\right)\left(3x-2\right)$

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 $nax^{n-1}$.

$$3\times 2x^{3-1}+2\left(-5\right)x^{2-1}+4x^{1-1}$$

Multiply $3$ times $2$.

$$6x^{3-1}+2\left(-5\right)x^{2-1}+4x^{1-1}$$

Subtract $1$ from $3$.

$$6x^{2}+2\left(-5\right)x^{2-1}+4x^{1-1}$$

Multiply $2$ times $-5$.

$$6x^{2}-10x^{2-1}+4x^{1-1}$$

Subtract $1$ from $2$.

$$6x^{2}-10x^{1}+4x^{1-1}$$

Subtract $1$ from $1$.

$$6x^{2}-10x^{1}+4x^{0}$$

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

$$6x^{2}-10x+4x^{0}$$

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

$$6x^{2}-10x+4\times 1$$

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

$$6x^{2}-10x+4$$

Evaluate

$2x^{3}-5x^{2}+4x+1$