Solve 1/15*x^6/6=

$$\frac { 1 } { 15 } \cdot \frac { x ^ { 6 } } { 6 } =$$

Evaluate

$$\frac{x^{6}}{90}$$

Solution Steps

Multiply \frac{1}{15} times \frac{x^{6}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{6}}{15\times 6}$$

Multiply 15 and 6 to get 90.

$$\frac{x^{6}}{90}$$

Differentiate w.r.t. x

$$\frac{x^{5}}{15}$$

Steps Using Definition of a Derivative

Multiply \frac{1}{15} times \frac{x^{6}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{15\times 6})$$

Multiply 15 and 6 to get 90.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{90})$$

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

$$6\times \frac{1}{90}x^{6-1}$$

Multiply 6 times \frac{1}{90}.

$$\frac{1}{15}x^{6-1}$$

Subtract 1 from 6.

$$\frac{1}{15}x^{5}$$