Solve j/dx=(x^2+1)^x^3

$$\frac { j } { d x } = ( x ^ { 2 } + 1 ) ^ { x ^ { 3 } }$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}\text{, }&x\neq -i\text{ and }x\neq i\text{ and }j\neq 0\text{ and }x\neq 0\\d\neq 0\text{, }&\left(x=i\text{ or }x=-i\right)\text{ and }j=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$j=dx\left(x^{2}+1\right)^{x^{3}}$$

Swap sides so that all variable terms are on the left hand side.

$$dx\left(x^{2}+1\right)^{x^{3}}=j$$

The equation is in standard form.

$$x\left(x^{2}+1\right)^{x^{3}}d=j$$

Divide both sides by x\left(x^{2}+1\right)^{x^{3}}.

$$\frac{x\left(x^{2}+1\right)^{x^{3}}d}{x\left(x^{2}+1\right)^{x^{3}}}=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}$$

Dividing by x\left(x^{2}+1\right)^{x^{3}} undoes the multiplication by x\left(x^{2}+1\right)^{x^{3}}.

$$d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}$$

Variable d cannot be equal to 0.

$$d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}\text{, }d\neq 0$$

Solve for d

$$d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}$$

$$x\neq 0\text{ and }j\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$j=dx\left(x^{2}+1\right)^{x^{3}}$$

Swap sides so that all variable terms are on the left hand side.

$$dx\left(x^{2}+1\right)^{x^{3}}=j$$

The equation is in standard form.

$$x\left(x^{2}+1\right)^{x^{3}}d=j$$

Divide both sides by x\left(x^{2}+1\right)^{x^{3}}.

$$\frac{x\left(x^{2}+1\right)^{x^{3}}d}{x\left(x^{2}+1\right)^{x^{3}}}=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}$$

Dividing by x\left(x^{2}+1\right)^{x^{3}} undoes the multiplication by x\left(x^{2}+1\right)^{x^{3}}.

$$d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}$$

Variable d cannot be equal to 0.

$$d=\frac{j}{x\left(x^{2}+1\right)^{x^{3}}}\text{, }d\neq 0$$

Solve for j

$$j=dx\left(x^{2}+1\right)^{x^{3}}$$

$$d\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{dx}j=\left(x^{2}+1\right)^{x^{3}}$$

Divide both sides by d^{-1}x^{-1}.

$$\frac{\frac{1}{dx}jdx}{1}=\frac{\left(x^{2}+1\right)^{x^{3}}dx}{1}$$

Dividing by d^{-1}x^{-1} undoes the multiplication by d^{-1}x^{-1}.

$$j=\frac{\left(x^{2}+1\right)^{x^{3}}dx}{1}$$

Divide \left(x^{2}+1\right)^{x^{3}} by d^{-1}x^{-1}.

$$j=dx\left(x^{2}+1\right)^{x^{3}}$$