Solve (-4y^frac{-8{15}})(-6y^frac{4{5}})

$$( - 4 y ^ { \frac { - 8 } { 15 } } ) ( - 6 y ^ { \frac { 4 } { 5 } } )$$

Evaluate

$$24y^{\frac{4}{15}}$$

Solution Steps

Fraction \frac{-8}{15} can be rewritten as -\frac{8}{15} by extracting the negative sign.

$$-4y^{-\frac{8}{15}}\left(-6\right)y^{\frac{4}{5}}$$

Multiply -4 and -6 to get 24.

$$24y^{-\frac{8}{15}}y^{\frac{4}{5}}$$

To multiply powers of the same base, add their exponents. Add -\frac{8}{15} and \frac{4}{5} to get \frac{4}{15}.

$$24y^{\frac{4}{15}}$$

Differentiate w.r.t. y

$$\frac{32}{5y^{\frac{11}{15}}}$$

Steps Using Definition of a Derivative

Fraction \frac{-8}{15} can be rewritten as -\frac{8}{15} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{-\frac{8}{15}}\left(-6\right)y^{\frac{4}{5}})$$

Multiply -4 and -6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}y}(24y^{-\frac{8}{15}}y^{\frac{4}{5}})$$

To multiply powers of the same base, add their exponents. Add -\frac{8}{15} and \frac{4}{5} to get \frac{4}{15}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(24y^{\frac{4}{15}})$$

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

$$\frac{4}{15}\times 24y^{\frac{4}{15}-1}$$

Multiply \frac{4}{15} times 24.

$$\frac{32}{5}y^{\frac{4}{15}-1}$$

Subtract 1 from \frac{4}{15}.

$$\frac{32}{5}y^{-\frac{11}{15}}$$