Exercise
$\frac{d}{dz}\left(\ln\left(4x+y^4+5z^2\right)=16+9xyz\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dz(ln(4x+y^45z^2)=16+9xyz). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the implicit derivative d/dz(ln(4x+y^45z^2)=16+9xyz)
Final answer to the exercise
$y^{\prime}=\frac{36xyz+9y^{5}z+45z^{3}y-4-4y^{\left(3+{\prime}\right)}+9y^{\left(4+{\prime}\right)}xz}{-9x\left(4x+5z^2\right)z}$