Solve {left(5x+3right)}^frac{2{3}}

$${ \left(5x+3 \right) }^{ \frac{ 2 }{ 3 } }$$

Differentiate w.r.t. x

$$\frac{10}{3\sqrt[3]{5x+3}}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$\frac{2}{3}\left(5x^{1}+3\right)^{\frac{2}{3}-1}\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}+3)$$

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}.

$$\frac{2}{3}\left(5x^{1}+3\right)^{-\frac{1}{3}}\times 5x^{1-1}$$

Simplify.

$$\frac{10}{3}x^{0}\left(5x^{1}+3\right)^{-\frac{1}{3}}$$

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

$$\frac{10}{3}x^{0}\left(5x+3\right)^{-\frac{1}{3}}$$

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

$$\frac{10}{3}\times 1\left(5x+3\right)^{-\frac{1}{3}}$$

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

$$\frac{10}{3}\left(5x+3\right)^{-\frac{1}{3}}$$

Evaluate

$$\left(5x+3\right)^{\frac{2}{3}}$$