Solve (b^3)^2+(b^2)^3

$$( b ^ { 3 } ) ^ { 2 } + ( b ^ { 2 } ) ^ { 3 }$$

Evaluate

$$2b^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$b^{6}+\left(b^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$b^{6}+b^{6}$$

Combine b^{6} and b^{6} to get 2b^{6}.

$$2b^{6}$$

Differentiate w.r.t. b

$$12b^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{6}+\left(b^{2}\right)^{3})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{6}+b^{6})$$

Combine b^{6} and b^{6} to get 2b^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{6})$$

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

$$6\times 2b^{6-1}$$

Multiply 6 times 2.

$$12b^{6-1}$$

Subtract 1 from 6.

$$12b^{5}$$