Solve 5ab-(-6a^2b)+(-3ab)-7ab+5

$$5 a b - ( - 6 a ^ { 2 } b ) + ( - 3 a b ) - 7 a b + 5$$

Differentiate w.r.t. a

$$b\left(12a-5\right)$$

Steps Using Derivative Rule for Sum

The opposite of -6a^{2}b is 6a^{2}b.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5ab+6a^{2}b-3ab-7ab+5)$$

Combine 5ab and -3ab to get 2ab.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2ab+6a^{2}b-7ab+5)$$

Combine 2ab and -7ab to get -5ab.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-5ab+6a^{2}b+5)$$

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}.

$$\left(-5b\right)a^{1-1}+2\times 6ba^{2-1}$$

Subtract 1 from 1.

$$\left(-5b\right)a^{0}+2\times 6ba^{2-1}$$

Multiply 2 times 6b.

$$\left(-5b\right)a^{0}+12ba^{2-1}$$

Subtract 1 from 2.

$$\left(-5b\right)a^{0}+12ba^{1}$$

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

$$\left(-5b\right)a^{0}+12ba$$

For any term t except 0, t^{0}=1.

$$\left(-5b\right)\times 1+12ba$$

For any term t, t\times 1=t and 1t=t.

$$-5b+12ba$$

Evaluate

$$5+6ba^{2}-5ab$$