Solve c_4^4*0.8^4*0.2^0=

$$c _ { 4 } ^ { 4 } \cdot 0.8 ^ { 4 } \cdot 0.2 ^ { 0 } =$$

Evaluate

$$\frac{256c_{4}^{4}}{625}$$

Solution Steps

Calculate 0.8 to the power of 4 and get 0.4096.

$$c_{4}^{4}\times 0.4096\times 0.2^{0}$$

Calculate 0.2 to the power of 0 and get 1.

$$c_{4}^{4}\times 0.4096\times 1$$

Multiply 0.4096 and 1 to get 0.4096.

$$c_{4}^{4}\times 0.4096$$

Differentiate w.r.t. c_4

$$\frac{1024c_{4}^{3}}{625}$$

Steps Using Definition of a Derivative

Calculate 0.8 to the power of 4 and get 0.4096.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}^{4}\times 0.4096\times 0.2^{0})$$

Calculate 0.2 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}^{4}\times 0.4096\times 1)$$

Multiply 0.4096 and 1 to get 0.4096.

$$\frac{\mathrm{d}}{\mathrm{d}c_{4}}(c_{4}^{4}\times 0.4096)$$

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

$$4\times 0.4096c_{4}^{4-1}$$

Multiply 4 times 0.4096.

$$1.6384c_{4}^{4-1}$$

Subtract 1 from 4.

$$1.6384c_{4}^{3}$$