Solve 6x^4+(-10x^4)+2x^4

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

Evaluate

$$-2x^{4}$$

Solution Steps

Combine 6x^{4} and -10x^{4} to get -4x^{4}.

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

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

$$-2x^{4}$$

Differentiate w.r.t. x

$$-8x^{3}$$

Steps Using Definition of a Derivative

Combine 6x^{4} and -10x^{4} to get -4x^{4}.

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

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

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

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

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

Multiply 4 times -2.

$$-8x^{4-1}$$

Subtract 1 from 4.

$$-8x^{3}$$