Exercise
$\frac{d}{dx}\left(\sin\left(5x+y\right)=3x\right)$
Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the implicit derivative d/dx(sin(5x+y)=3x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.
Find the implicit derivative d/dx(sin(5x+y)=3x)
Final answer to the exercise
$y^{\prime}=3\sec\left(5x+y\right)-5$