Solve (4x+3)^frac{3{4}}

$$( 4 x + 3 ) ^ { \frac { 3 } { 4 } }$$

Differentiate w.r.t. x

$$\frac{3}{\sqrt[4]{4x+3}}$$

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).

$$\frac{3}{4}\left(4x^{1}+3\right)^{\frac{3}{4}-1}\frac{\mathrm{d}}{\mathrm{d}x}(4x^{1}+3)$$

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}.

$$\frac{3}{4}\left(4x^{1}+3\right)^{-\frac{1}{4}}\times 4x^{1-1}$$

Simplify.

$$3x^{0}\left(4x^{1}+3\right)^{-\frac{1}{4}}$$

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

$$3x^{0}\left(4x+3\right)^{-\frac{1}{4}}$$

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

$$3\times 1\left(4x+3\right)^{-\frac{1}{4}}$$

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

$$3\left(4x+3\right)^{-\frac{1}{4}}$$

Evaluate

$$\left(4x+3\right)^{\frac{3}{4}}$$