Solve 4(M)^(3)-4(M)^(2)-M-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

$$4 { M }^{ 3 } -4 { M }^{ 2 } -M-1$$

Differentiate w.r.t. M

$12M^{2}-8M-1$

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 $nax^{n-1}$.

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

Multiply $3$ times $4$.

$$12M^{3-1}+2\left(-4\right)M^{2-1}-M^{1-1}$$

Subtract $1$ from $3$.

$$12M^{2}+2\left(-4\right)M^{2-1}-M^{1-1}$$

Multiply $2$ times $-4$.

$$12M^{2}-8M^{2-1}-M^{1-1}$$

Subtract $1$ from $2$.

$$12M^{2}-8M^{1}-M^{1-1}$$

Subtract $1$ from $1$.

$$12M^{2}-8M^{1}-M^{0}$$

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

$$12M^{2}-8M-M^{0}$$

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

$$12M^{2}-8M-1$$

Evaluate

$4M^{3}-4M^{2}-M-1$