Solve g[(3^2+sqrt[3]{8}-1^12345)*(sqrt{100}+sqrt{81})]

$$g [ ( 3 ^ { 2 } + \sqrt[ 3 ] { 8 } - 1 ^ { 12345 } ) \cdot ( \sqrt { 100 } + \sqrt { 81 } ) ]$$

Evaluate

$$190g$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$g\left(9+\sqrt[3]{8}-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right)$$

Calculate \sqrt[3]{8} and get 2.

$$g\left(9+2-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right)$$

Add 9 and 2 to get 11.

$$g\left(11-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right)$$

Calculate 1 to the power of 12345 and get 1.

$$g\left(11-1\right)\left(\sqrt{100}+\sqrt{81}\right)$$

Subtract 1 from 11 to get 10.

$$g\times 10\left(\sqrt{100}+\sqrt{81}\right)$$

Calculate the square root of 100 and get 10.

$$g\times 10\left(10+\sqrt{81}\right)$$

Calculate the square root of 81 and get 9.

$$g\times 10\left(10+9\right)$$

Add 10 and 9 to get 19.

$$g\times 10\times 19$$

Multiply 10 and 19 to get 190.

$$g\times 190$$

Differentiate w.r.t. g

$$190$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\left(9+\sqrt[3]{8}-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right))$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\left(9+2-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right))$$

Add 9 and 2 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\left(11-1^{12345}\right)\left(\sqrt{100}+\sqrt{81}\right))$$

Calculate 1 to the power of 12345 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\left(11-1\right)\left(\sqrt{100}+\sqrt{81}\right))$$

Subtract 1 from 11 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times 10\left(\sqrt{100}+\sqrt{81}\right))$$

Calculate the square root of 100 and get 10.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times 10\left(10+\sqrt{81}\right))$$

Calculate the square root of 81 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times 10\left(10+9\right))$$

Add 10 and 9 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times 10\times 19)$$

Multiply 10 and 19 to get 190.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times 190)$$

The derivative of ax^{n} is nax^{n-1}.

$$190g^{1-1}$$

Subtract 1 from 1.

$$190g^{0}$$

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

$$190\times 1$$

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

$$190$$