Solve 3x ^ 3 + 5x ^ 2 - 17x ^ 2 + 10 | 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

$$3x^{3}+5x^{2}-17x^{2}+10$$

Differentiate w.r.t. x

$3x\left(3x-8\right)$

Steps Using Derivative Rule for Sum

Combine $5x^{2}$ and $-17x^{2}$ to get $-12x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-12x^{2}+10)$$

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 $nax^{n-1}$.

$$3\times 3x^{3-1}+2\left(-12\right)x^{2-1}$$

Multiply $3$ times $3$.

$$9x^{3-1}+2\left(-12\right)x^{2-1}$$

Subtract $1$ from $3$.

$$9x^{2}+2\left(-12\right)x^{2-1}$$

Multiply $2$ times $-12$.

$$9x^{2}-24x^{2-1}$$

Subtract $1$ from $2$.

$$9x^{2}-24x^{1}$$

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

$$9x^{2}-24x$$

Evaluate

$3x^{3}-12x^{2}+10$