Solve (1/2Theta3/8)*16

$$( \frac { 1 } { 2 } \Theta \frac { 3 } { 8 } ) \times 16$$

Evaluate

$$3\Theta$$

Solution Steps

Multiply \frac{1}{2} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{2\times 8}\Theta \times 16$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 8}.

$$\frac{3}{16}\Theta \times 16$$

Cancel out 16 and 16.

$$3\Theta$$

Differentiate w.r.t. Θ

$$3$$

Steps Using Definition of a Derivative

Multiply \frac{1}{2} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}\Theta }(\frac{1\times 3}{2\times 8}\Theta \times 16)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}\Theta }(\frac{3}{16}\Theta \times 16)$$

Cancel out 16 and 16.

$$\frac{\mathrm{d}}{\mathrm{d}\Theta }(3\Theta )$$

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

$$3\Theta ^{1-1}$$

Subtract 1 from 1.

$$3\Theta ^{0}$$

For any term t except 0, t^{0}=1.

$$3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3$$