Solve 10^5x^7/2

$$\frac { 10 ^ { 5 } x ^ { 7 } } { 2 }$$

Evaluate

$$50000x^{7}$$

Solution Steps

Calculate 10 to the power of 5 and get 100000.

$$\frac{100000x^{7}}{2}$$

Divide 100000x^{7} by 2 to get 50000x^{7}.

$$50000x^{7}$$

Differentiate w.r.t. x

$$350000x^{6}$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 5 and get 100000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{100000x^{7}}{2})$$

Divide 100000x^{7} by 2 to get 50000x^{7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(50000x^{7})$$

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

$$7\times 50000x^{7-1}$$

Multiply 7 times 50000.

$$350000x^{7-1}$$

Subtract 1 from 7.

$$350000x^{6}$$