Solve - x ^ 2 + 4x ^ 2 - 8x ^ 2 + 11x ^ 2 | 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

$$-x^{2}+4x^{2}-8x^{2}+11x^{2}$$

Evaluate

$6x^{2}$

Solution Steps

Combine $4x^{2}$ and $-8x^{2}$ to get $-4x^{2}$.

$$-x^{2}-4x^{2}+11x^{2}$$

Combine $-4x^{2}$ and $11x^{2}$ to get $7x^{2}$.

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

Combine $-x^{2}$ and $7x^{2}$ to get $6x^{2}$.

$$6x^{2}$$

Differentiate w.r.t. x

$12x$

Steps Using Definition of a Derivative

Combine $4x^{2}$ and $-8x^{2}$ to get $-4x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}-4x^{2}+11x^{2})$$

Combine $-4x^{2}$ and $11x^{2}$ to get $7x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+7x^{2})$$

Combine $-x^{2}$ and $7x^{2}$ to get $6x^{2}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$2\times 6x^{2-1}$$

Multiply $2$ times $6$.

$$12x^{2-1}$$

Subtract $1$ from $2$.

$$12x^{1}$$

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

$$12x$$