Solve 5x^6-2x^6*3x^6:(-2x^6)=

$$5 x ^ { 6 } - 2 x ^ { 6 } \cdot 3 x ^ { 6 } : ( - 2 x ^ { 6 } ) =$$

Evaluate

$$8x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$5x^{6}-\frac{2x^{12}\times 3}{-2x^{6}}$$

Cancel out 2x^{6} in both numerator and denominator.

$$5x^{6}-\frac{3x^{6}}{-1}$$

Anything divided by -1 gives its opposite.

$$5x^{6}-\left(-3x^{6}\right)$$

The opposite of -3x^{6} is 3x^{6}.

$$5x^{6}+3x^{6}$$

Combine 5x^{6} and 3x^{6} to get 8x^{6}.

$$8x^{6}$$

Differentiate w.r.t. x

$$48x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}-\frac{2x^{12}\times 3}{-2x^{6}})$$

Cancel out 2x^{6} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}-\frac{3x^{6}}{-1})$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}-\left(-3x^{6}\right))$$

The opposite of -3x^{6} is 3x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}+3x^{6})$$

Combine 5x^{6} and 3x^{6} to get 8x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{6})$$

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

$$6\times 8x^{6-1}$$

Multiply 6 times 8.

$$48x^{6-1}$$

Subtract 1 from 6.

$$48x^{5}$$