Solve 2x^3+3*2^2+6*5-100:2^2

$$2 x ^ { 3 } + 3 \cdot 2 ^ { 2 } + 6 \cdot 5 - 100 : 2 ^ { 2 }$$

Evaluate

$$2x^{3}+17$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$2x^{3}+3\times 4+6\times 5-\frac{100}{2^{2}}$$

Multiply 3 and 4 to get 12.

$$2x^{3}+12+6\times 5-\frac{100}{2^{2}}$$

Multiply 6 and 5 to get 30.

$$2x^{3}+12+30-\frac{100}{2^{2}}$$

Add 12 and 30 to get 42.

$$2x^{3}+42-\frac{100}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$2x^{3}+42-\frac{100}{4}$$

Divide 100 by 4 to get 25.

$$2x^{3}+42-25$$

Subtract 25 from 42 to get 17.

$$2x^{3}+17$$

Differentiate w.r.t. x

$$6x^{2}$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+3\times 4+6\times 5-\frac{100}{2^{2}})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+12+6\times 5-\frac{100}{2^{2}})$$

Multiply 6 and 5 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+12+30-\frac{100}{2^{2}})$$

Add 12 and 30 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+42-\frac{100}{2^{2}})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+42-\frac{100}{4})$$

Divide 100 by 4 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+42-25)$$

Subtract 25 from 42 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+17)$$

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.

$$6x^{2}$$