Solve (3m-sqrt{25-9})*(3m+sqrt{11+4+1})=

$$( 3 m - \sqrt { 25 - 9 } ) \cdot ( 3 m + \sqrt { 11 + 4 + 1 } ) =$$

Evaluate

$$9m^{2}-16$$

Solution Steps

Subtract 9 from 25 to get 16.

$$\left(3m-\sqrt{16}\right)\left(3m+\sqrt{11+4+1}\right)$$

Calculate the square root of 16 and get 4.

$$\left(3m-4\right)\left(3m+\sqrt{11+4+1}\right)$$

Add 11 and 4 to get 15.

$$\left(3m-4\right)\left(3m+\sqrt{15+1}\right)$$

Add 15 and 1 to get 16.

$$\left(3m-4\right)\left(3m+\sqrt{16}\right)$$

Calculate the square root of 16 and get 4.

$$\left(3m-4\right)\left(3m+4\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(3m\right)^{2}-4^{2}$$

Expand \left(3m\right)^{2}.

$$3^{2}m^{2}-4^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9m^{2}-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$9m^{2}-16$$

Differentiate w.r.t. m

$$18m$$

Steps Using Derivative Rule for Sum

Subtract 9 from 25 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m-\sqrt{16}\right)\left(3m+\sqrt{11+4+1}\right))$$

Calculate the square root of 16 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m-4\right)\left(3m+\sqrt{11+4+1}\right))$$

Add 11 and 4 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m-4\right)\left(3m+\sqrt{15+1}\right))$$

Add 15 and 1 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m-4\right)\left(3m+\sqrt{16}\right))$$

Calculate the square root of 16 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m-4\right)\left(3m+4\right))$$

Consider \left(3m-4\right)\left(3m+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(3m\right)^{2}-4^{2})$$

Expand \left(3m\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(3^{2}m^{2}-4^{2})$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}m}(9m^{2}-4^{2})$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}m}(9m^{2}-16)$$

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}.

$$2\times 9m^{2-1}$$

Multiply 2 times 9.

$$18m^{2-1}$$

Subtract 1 from 2.

$$18m^{1}$$

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

$$18m$$