Solve 3q^4*2q^5/q^3

$$\frac { 3 q ^ { 4 } \times 2 q ^ { 5 } } { q ^ { 3 } }$$

Evaluate

$$6q^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{3q^{9}\times 2}{q^{3}}$$

Cancel out q^{3} in both numerator and denominator.

$$2\times 3q^{6}$$

Multiply 2 and 3 to get 6.

$$6q^{6}$$

Differentiate w.r.t. q

$$36q^{5}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}q}(\frac{6q^{5}}{1}q^{4-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}q}(6q^{5}q^{1})$$

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}.

$$6q^{5}q^{1-1}$$

Do the arithmetic.

$$6q^{5}q^{0}$$

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

$$6q^{5}\times 1$$

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

$$6q^{5}$$