Solve 2x^3-6^2-5^6

$$2 x ^ { 3 } - 6 ^ { 2 } - 5 ^ { 6 }$$

Evaluate

$$2x^{3}-15661$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$2x^{3}-36-5^{6}$$

Calculate 5 to the power of 6 and get 15625.

$$2x^{3}-36-15625$$

Subtract 15625 from -36 to get -15661.

$$2x^{3}-15661$$

Differentiate w.r.t. x

$$6x^{2}$$

Steps Using Derivative Rule for Sum

Calculate 6 to the power of 2 and get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-36-5^{6})$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-36-15625)$$

Subtract 15625 from -36 to get -15661.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-15661)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 2x^{3-1}$$

Multiply 3 times 2.

$$6x^{3-1}$$

Subtract 1 from 3.

$$6x^{2}$$