Solve 66+4^2+26^2-4+3a^2-206

$$66 + 4 ^ { 2 } + 26 ^ { 2 } - 4 + 3 a ^ { 2 } - 206$$

Evaluate

$$3a^{2}+548$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$66+16+26^{2}-4+3a^{2}-206$$

Add 66 and 16 to get 82.

$$82+26^{2}-4+3a^{2}-206$$

Calculate 26 to the power of 2 and get 676.

$$82+676-4+3a^{2}-206$$

Add 82 and 676 to get 758.

$$758-4+3a^{2}-206$$

Subtract 4 from 758 to get 754.

$$754+3a^{2}-206$$

Subtract 206 from 754 to get 548.

$$548+3a^{2}$$

Differentiate w.r.t. a

$$6a$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(66+16+26^{2}-4+3a^{2}-206)$$

Add 66 and 16 to get 82.

$$\frac{\mathrm{d}}{\mathrm{d}a}(82+26^{2}-4+3a^{2}-206)$$

Calculate 26 to the power of 2 and get 676.

$$\frac{\mathrm{d}}{\mathrm{d}a}(82+676-4+3a^{2}-206)$$

Add 82 and 676 to get 758.

$$\frac{\mathrm{d}}{\mathrm{d}a}(758-4+3a^{2}-206)$$

Subtract 4 from 758 to get 754.

$$\frac{\mathrm{d}}{\mathrm{d}a}(754+3a^{2}-206)$$

Subtract 206 from 754 to get 548.

$$\frac{\mathrm{d}}{\mathrm{d}a}(548+3a^{2})$$

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}.

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

Multiply 2 times 3.

$$6a^{2-1}$$

Subtract 1 from 2.

$$6a^{1}$$

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

$$6a$$