Solve frac{p^{0}lambda^r^0}{q^0}sqrt{50^0}

$$\frac { p ^ { 0 } \lambda ^ { r ^ { 0 } } } { q ^ { 0 } } \sqrt { 50 ^ { 0 } }$$

Evaluate

$$\lambda$$

Solution Steps

Calculate p to the power of 0 and get 1.

$$\frac{1\lambda ^{r^{0}}}{q^{0}}\sqrt{50^{0}}$$

Calculate r to the power of 0 and get 1.

$$\frac{1\lambda ^{1}}{q^{0}}\sqrt{50^{0}}$$

Calculate \lambda to the power of 1 and get \lambda .

$$\frac{1\lambda }{q^{0}}\sqrt{50^{0}}$$

Calculate q to the power of 0 and get 1.

$$\frac{1\lambda }{1}\sqrt{50^{0}}$$

Cancel out 1 and 1.

$$\lambda \sqrt{50^{0}}$$

Calculate 50 to the power of 0 and get 1.

$$\lambda \sqrt{1}$$

Calculate the square root of 1 and get 1.

$$\lambda \times 1$$

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

$$\lambda$$

Differentiate w.r.t. λ

$$1$$

Steps Using Definition of a Derivative

Calculate p to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\frac{1\lambda ^{r^{0}}}{q^{0}}\sqrt{50^{0}})$$

Calculate r to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\frac{1\lambda ^{1}}{q^{0}}\sqrt{50^{0}})$$

Calculate \lambda to the power of 1 and get \lambda .

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\frac{1\lambda }{q^{0}}\sqrt{50^{0}})$$

Calculate q to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\frac{1\lambda }{1}\sqrt{50^{0}})$$

Cancel out 1 and 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\lambda \sqrt{50^{0}})$$

Calculate 50 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\lambda \sqrt{1})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}\lambda }(\lambda \times 1)$$

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

$$\lambda ^{1-1}$$

Subtract 1 from 1.

$$\lambda ^{0}$$

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

$$1$$