Solve f(x) = 2x ^ 3 - 2x ^ 2 - 36x + 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

$$f(x)=2x^{3}-2x^{2}-36x+3$$

Differentiate w.r.t. x

$6x^{2}-4x-36$

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 $nax^{n-1}$.

$$3\times 2x^{3-1}+2\left(-2\right)x^{2-1}-36x^{1-1}$$

Multiply $3$ times $2$.

$$6x^{3-1}+2\left(-2\right)x^{2-1}-36x^{1-1}$$

Subtract $1$ from $3$.

$$6x^{2}+2\left(-2\right)x^{2-1}-36x^{1-1}$$

Multiply $2$ times $-2$.

$$6x^{2}-4x^{2-1}-36x^{1-1}$$

Subtract $1$ from $2$.

$$6x^{2}-4x^{1}-36x^{1-1}$$

Subtract $1$ from $1$.

$$6x^{2}-4x^{1}-36x^{0}$$

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

$$6x^{2}-4x-36x^{0}$$

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

$$6x^{2}-4x-36$$

Evaluate

$2x^{3}-2x^{2}-36x+3$