Solve 1/2[x^6/6]_0^pi/2+[xnmux]_0^pi/2+[0uvx]_0^pi/2

$$\frac { 1 } { 2 } [ \frac { x ^ { 6 } } { 6 } ] _ { 0 } ^ { \pi / 2 } + [ x n \mu x ] _ { 0 } ^ { \pi / 2 } + [ 0 u v x ] _ { 0 } ^ { \pi / 2 }$$

Evaluate

$$\frac{x^{6}}{12}$$

Solution Steps

Multiply \frac{1}{2} times \frac{x^{6}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{6}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{x^{6}}{12}$$

Differentiate w.r.t. x

$$\frac{x^{5}}{2}$$

Steps Using Definition of a Derivative

Multiply \frac{1}{2} times \frac{x^{6}}{6} by multiplying numerator times numerator and denominator times denominator.

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

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{12})$$

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

$$6\times \frac{1}{12}x^{6-1}$$

Multiply 6 times \frac{1}{12}.

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

Subtract 1 from 6.

$$\frac{1}{2}x^{5}$$