Solve 54-6a*9a+12*15*30+64*77-69

$$54 - 6 a \cdot 9 a + 12 \cdot 15 \cdot 30 + 64 \cdot 77 - 69$$

Evaluate

$$10313-54a^{2}$$

Solution Steps

Multiply a and a to get a^{2}.

$$54-6a^{2}\times 9+12\times 15\times 30+64\times 77-69$$

Multiply 12 and 15 to get 180. Multiply 64 and 77 to get 4928.

$$54-6a^{2}\times 9+180\times 30+4928-69$$

Multiply 6 and 9 to get 54.

$$54-54a^{2}+180\times 30+4928-69$$

Multiply 180 and 30 to get 5400.

$$54-54a^{2}+5400+4928-69$$

Add 54 and 5400 to get 5454.

$$5454-54a^{2}+4928-69$$

Add 5454 and 4928 to get 10382.

$$10382-54a^{2}-69$$

Subtract 69 from 10382 to get 10313.

$$10313-54a^{2}$$

Differentiate w.r.t. a

$$-108a$$

Steps Using Derivative Rule for Sum

Multiply a and a to get a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(54-6a^{2}\times 9+12\times 15\times 30+64\times 77-69)$$

Multiply 12 and 15 to get 180. Multiply 64 and 77 to get 4928.

$$\frac{\mathrm{d}}{\mathrm{d}a}(54-6a^{2}\times 9+180\times 30+4928-69)$$

Multiply 6 and 9 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}a}(54-54a^{2}+180\times 30+4928-69)$$

Multiply 180 and 30 to get 5400.

$$\frac{\mathrm{d}}{\mathrm{d}a}(54-54a^{2}+5400+4928-69)$$

Add 54 and 5400 to get 5454.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5454-54a^{2}+4928-69)$$

Add 5454 and 4928 to get 10382.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10382-54a^{2}-69)$$

Subtract 69 from 10382 to get 10313.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10313-54a^{2})$$

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}.

$$2\left(-54\right)a^{2-1}$$

Multiply 2 times -54.

$$-108a^{2-1}$$

Subtract 1 from 2.

$$-108a^{1}$$

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

$$-108a$$